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- (x^2-2x+3)^2-2(x-2)(2x^2-10x-9)=0
- (x^2-2x-3)^2-2(x-2)(2x^2-10x+9)=0
- (x^2-2x+3)^2-2(x+2)(2x^2-10x+9)=0
- (x^2-2x+3)^2+2(x-2)(2x^2-10x+9)=0
(x^2-2x+3)^2-2(x-2)(2x^2-10x+9)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 2 \ / 2 \ \x - 2*x + 3/ - 2*(x - 2)*\2*x - 10*x + 9/ = 0
$$- 2 \left(x - 2\right) \left(\left(2 x^{2} - 10 x\right) + 9\right) + \left(\left(x^{2} - 2 x\right) + 3\right)^{2} = 0$$
Suma y producto de raíces
[src]
suma
_______________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________
/ ____________________ / ____________________ / ____________________ / ____________________
/ / _______ / / _______ / / _______ / / _______
/ 56 36 / 1291 I*\/ 66135 152 / 56 / 1291 I*\/ 66135 36 152 / 56 / 1291 I*\/ 66135 36 152 / 56 36 / 1291 I*\/ 66135 152
I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + --------------------------- I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + --------------------------- I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + --------------------------- I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + ---------------------------
__________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________ __________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________ __________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________ __________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________
/ ____________________ / / ____________________ / _______ / ____________________ / / ____________________ / _______ / ____________________ / / ____________________ / _______ / ____________________ / / ____________________ / _______
/ / _______ / / / _______ / 1291 I*\/ 66135 / / _______ / / / _______ / 1291 I*\/ 66135 / / _______ / / / _______ / 1291 I*\/ 66135 / / _______ / / / _______ / 1291 I*\/ 66135
/ 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + -----------
/ - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12
/ 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________
/ / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______
/ / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135
/ 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- / 9*3 / ---- + ----------- / / 9*3 / ---- + -----------
\/ \/ 108 12 \/ \/ \/ 108 12 \/ \/ 108 12 \/ \/ \/ 108 12 \/ \/ 108 12 \/ \/ \/ 108 12 \/ \/ 108 12 \/ \/ \/ 108 12
2 - ---------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2 + ---------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2 + ---------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2 - ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
$$\left(\left(\left(2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right) + \left(2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right)\right) + \left(2 + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right)\right) + \left(2 - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right)$$
=
8
$$8$$
producto
/ _______________________________________________________________________________________________________________________________________________\ / _______________________________________________________________________________________________________________________________________________\ / _______________________________________________________________________________________________________________________________________________\ / _______________________________________________________________________________________________________________________________________________\ | / ____________________ | | / ____________________ | | / ____________________ | | / ____________________ | | / / _______ | | / / _______ | | / / _______ | | / / _______ | | / 56 36 / 1291 I*\/ 66135 152 | | / 56 / 1291 I*\/ 66135 36 152 | | / 56 / 1291 I*\/ 66135 36 152 | | / 56 36 / 1291 I*\/ 66135 152 | | I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + --------------------------- | | I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + --------------------------- | | I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + --------------------------- | | I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + --------------------------- | | __________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________ | | __________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________ | | __________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________ | | __________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________ | | / ____________________ / / ____________________ / _______ | | / ____________________ / / ____________________ / _______ | | / ____________________ / / ____________________ / _______ | | / ____________________ / / ____________________ / _______ | | / / _______ / / / _______ / 1291 I*\/ 66135 | | / / _______ / / / _______ / 1291 I*\/ 66135 | | / / _______ / / / _______ / 1291 I*\/ 66135 | | / / _______ / / / _______ / 1291 I*\/ 66135 | | / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- | | / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- | | / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- | | / 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + ----------- | | / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 | | / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 | | / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 | | / - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12 | | / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ | | / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ | | / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ | | / 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 | | / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 | | / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 | | / / 1291 I*\/ 66135 / / / 1291 I*\/ 66135 | | / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- | | / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- | | / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- | | / 9*3 / ---- + ----------- / / 9*3 / ---- + ----------- | | \/ \/ 108 12 \/ \/ \/ 108 12 | | \/ \/ 108 12 \/ \/ \/ 108 12 | | \/ \/ 108 12 \/ \/ \/ 108 12 | | \/ \/ 108 12 \/ \/ \/ 108 12 | |2 - ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------|*|2 + ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------|*|2 + ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------|*|2 - ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right) \left(2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right) \left(2 + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right) \left(2 - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}\right)$$
=
45
$$45$$
45
Respuesta rápida
[src]
_______________________________________________________________________________________________________________________________________________
/ ____________________
/ / _______
/ 56 36 / 1291 I*\/ 66135 152
I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + ---------------------------
__________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________
/ ____________________ / / ____________________ / _______
/ / _______ / / / _______ / 1291 I*\/ 66135
/ 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + -----------
/ - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12
/ 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________
/ / _______ / / / _______
/ / 1291 I*\/ 66135 / / / 1291 I*\/ 66135
/ 9*3 / ---- + ----------- / / 9*3 / ---- + -----------
\/ \/ 108 12 \/ \/ \/ 108 12
x1 = 2 - ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = 2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}$$
_______________________________________________________________________________________________________________________________________________
/ ____________________
/ / _______
/ 56 / 1291 I*\/ 66135 36 152
I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + ---------------------------
__________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________
/ ____________________ / / ____________________ / _______
/ / _______ / / / _______ / 1291 I*\/ 66135
/ 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + -----------
/ - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12
/ 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________
/ / _______ / / / _______
/ / 1291 I*\/ 66135 / / / 1291 I*\/ 66135
/ 9*3 / ---- + ----------- / / 9*3 / ---- + -----------
\/ \/ 108 12 \/ \/ \/ 108 12
x2 = 2 + ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{2} = 2 - \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}$$
_______________________________________________________________________________________________________________________________________________
/ ____________________
/ / _______
/ 56 / 1291 I*\/ 66135 36 152
I* / -- + 2*3 / ---- + ----------- + ---------------------------------------------------------------------------- + ---------------------------
__________________________________________________________________ / 3 \/ 108 12 __________________________________________________________________ ____________________
/ ____________________ / / ____________________ / _______
/ / _______ / / / _______ / 1291 I*\/ 66135
/ 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + -----------
/ - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12
/ 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________
/ / _______ / / / _______
/ / 1291 I*\/ 66135 / / / 1291 I*\/ 66135
/ 9*3 / ---- + ----------- / / 9*3 / ---- + -----------
\/ \/ 108 12 \/ \/ \/ 108 12
x3 = 2 + ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{3} = 2 + \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}$$
_______________________________________________________________________________________________________________________________________________
/ ____________________
/ / _______
/ 56 36 / 1291 I*\/ 66135 152
I* / -- - ---------------------------------------------------------------------------- + 2*3 / ---- + ----------- + ---------------------------
__________________________________________________________________ / 3 __________________________________________________________________ \/ 108 12 ____________________
/ ____________________ / / ____________________ / _______
/ / _______ / / / _______ / 1291 I*\/ 66135
/ 28 / 1291 I*\/ 66135 152 / / 28 / 1291 I*\/ 66135 152 9*3 / ---- + -----------
/ - -- + 2*3 / ---- + ----------- + --------------------------- / / - -- + 2*3 / ---- + ----------- + --------------------------- \/ 108 12
/ 3 \/ 108 12 ____________________ / / 3 \/ 108 12 ____________________
/ / _______ / / / _______
/ / 1291 I*\/ 66135 / / / 1291 I*\/ 66135
/ 9*3 / ---- + ----------- / / 9*3 / ---- + -----------
\/ \/ 108 12 \/ \/ \/ 108 12
x4 = 2 - ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{4} = 2 - \frac{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2} + \frac{i \sqrt{\frac{56}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} - \frac{36}{\sqrt{- \frac{28}{3} + \frac{152}{9 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}} + 2 \sqrt[3]{\frac{1291}{108} + \frac{\sqrt{66135} i}{12}}}}{2}$$
x4 = 2 - sqrt(-28/3 + 152/(9*(1291/108 + sqrt(66135)*i/12)^(1/3)) + 2*(1291/108 + sqrt(66135)*i/12)^(1/3))/2 + i*sqrt(56/3 + 152/(9*(1291/108 + sqrt(66135)*i/12)^(1/3)) - 36/sqrt(-28/3 + 152/(9*(1291/108 + sqrt(66135)*i/12)^(1/3)) + 2*(1291/108 + sqrt(66135)*i/12)^(1/3)) + 2*(1291/108 + sqrt(66135)*i/12)^(1/3))/2
Respuesta numérica
[src]
x1 = 1.37356986325353 - 0.457003587298789*i
x2 = 1.37356986325353 + 0.457003587298789*i
x3 = 2.62643013674647 - 3.81784980763315*i
x4 = 2.62643013674647 + 3.81784980763315*i
x4 = 2.62643013674647 + 3.81784980763315*i