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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
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Ecuación -4*(-z+7)=z+17
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- sqrt^ cuatro (17x^ dos - dieciséis)=x
- raíz cuadrada de en el grado 4(17x al cuadrado menos 16) es igual a x
- raíz cuadrada de en el grado cuatro (17x en el grado dos menos dieciséis) es igual a x
- √^4(17x^2-16)=x
- sqrt4(17x2-16)=x
- sqrt417x2-16=x
- sqrt⁴(17x²-16)=x
- sqrt en el grado 4(17x en el grado 2-16)=x
- sqrt^417x^2-16=x
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Expresiones semejantes
- sqrt^4(17x^2+16)=x
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(0,5+(sinx)^2)+c0s2x=1
- sqrt4(4x+5-x^2)-sqrt(4x-x^2-3)=1
- sqrt(log(cos(x)))=0
- sqrt(xx+16)=3x-4
- sqrt(x+7)-sqrt(x-7)=4
sqrt^4(17x^2-16)=x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 ____________ / 2 \/ 17*x - 16 = x
$$\left(\sqrt{17 x^{2} - 16}\right)^{4} = x$$
Respuesta rápida
[src]
x1 = 1
$$x_{1} = 1$$
___________________ / ___________________ \
/ ____ | / ____ |
/ 4039 19*\/ 33 | ___ / 4039 19*\/ 33 |
3 / ----- + --------- | \/ 3 *3 / ----- + --------- ___ |
1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 |
x2 = - - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------|
3 ___________________ 2 | 2 ___________________|
/ ____ | / ____ |
/ 4039 19*\/ 33 | / 4039 19*\/ 33 |
153*3 / ----- + --------- | 153*3 / ----- + --------- |
\/ 15606 5202 \ \/ 15606 5202 /
$$x_{2} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)$$
___________________ / ___________________ \
/ ____ | / ____ |
/ 4039 19*\/ 33 | ___ / 4039 19*\/ 33 |
3 / ----- + --------- |\/ 3 *3 / ----- + --------- ___ |
1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 |
x3 = - - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------|
3 ___________________ 2 | 2 ___________________|
/ ____ | / ____ |
/ 4039 19*\/ 33 | / 4039 19*\/ 33 |
153*3 / ----- + --------- | 153*3 / ----- + --------- |
\/ 15606 5202 \ \/ 15606 5202 /
$$x_{3} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)$$
___________________
/ ____
1 / 4039 19*\/ 33 62
x4 = - - + 3 / ----- + --------- + ----------------------------
3 \/ 15606 5202 ___________________
/ ____
/ 4039 19*\/ 33
153*3 / ----- + ---------
\/ 15606 5202
$$x_{4} = - \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}$$
x4 = -1/3 + 62/(153*(19*sqrt(33)/5202 + 4039/15606)^(1/3)) + (19*sqrt(33)/5202 + 4039/15606)^(1/3)
Suma y producto de raíces
[src]
suma
___________________ / ___________________ \ ___________________ / ___________________ \
/ ____ | / ____ | / ____ | / ____ |
/ 4039 19*\/ 33 | ___ / 4039 19*\/ 33 | / 4039 19*\/ 33 | ___ / 4039 19*\/ 33 | ___________________
3 / ----- + --------- | \/ 3 *3 / ----- + --------- ___ | 3 / ----- + --------- |\/ 3 *3 / ----- + --------- ___ | / ____
1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 | 1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 | 1 / 4039 19*\/ 33 62
1 + - - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------| + - - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------| + - - + 3 / ----- + --------- + ----------------------------
3 ___________________ 2 | 2 ___________________| 3 ___________________ 2 | 2 ___________________| 3 \/ 15606 5202 ___________________
/ ____ | / ____ | / ____ | / ____ | / ____
/ 4039 19*\/ 33 | / 4039 19*\/ 33 | / 4039 19*\/ 33 | / 4039 19*\/ 33 | / 4039 19*\/ 33
153*3 / ----- + --------- | 153*3 / ----- + --------- | 153*3 / ----- + --------- | 153*3 / ----- + --------- | 153*3 / ----- + ---------
\/ 15606 5202 \ \/ 15606 5202 / \/ 15606 5202 \ \/ 15606 5202 / \/ 15606 5202
$$\left(- \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}\right) + \left(\left(1 + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)\right)\right) + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)\right)\right)$$
=
/ ___________________ \ / ___________________ \ | / ____ | | / ____ | | ___ / 4039 19*\/ 33 | | ___ / 4039 19*\/ 33 | |\/ 3 *3 / ----- + --------- ___ | | \/ 3 *3 / ----- + --------- ___ | | \/ 15606 5202 31*\/ 3 | | \/ 15606 5202 31*\/ 3 | I*|------------------------------ - ----------------------------| + I*|- ------------------------------ + ----------------------------| | 2 ___________________| | 2 ___________________| | / ____ | | / ____ | | / 4039 19*\/ 33 | | / 4039 19*\/ 33 | | 153*3 / ----- + --------- | | 153*3 / ----- + --------- | \ \/ 15606 5202 / \ \/ 15606 5202 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right) + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)$$
producto
/ ___________________ / ___________________ \\ / ___________________ / ___________________ \\ | / ____ | / ____ || | / ____ | / ____ || | / 4039 19*\/ 33 | ___ / 4039 19*\/ 33 || | / 4039 19*\/ 33 | ___ / 4039 19*\/ 33 || / ___________________ \ | 3 / ----- + --------- | \/ 3 *3 / ----- + --------- ___ || | 3 / ----- + --------- |\/ 3 *3 / ----- + --------- ___ || | / ____ | | 1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 || | 1 31 \/ 15606 5202 | \/ 15606 5202 31*\/ 3 || | 1 / 4039 19*\/ 33 62 | |- - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------||*|- - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------||*|- - + 3 / ----- + --------- + ----------------------------| | 3 ___________________ 2 | 2 ___________________|| | 3 ___________________ 2 | 2 ___________________|| | 3 \/ 15606 5202 ___________________| | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 4039 19*\/ 33 | / 4039 19*\/ 33 || | / 4039 19*\/ 33 | / 4039 19*\/ 33 || | / 4039 19*\/ 33 | | 153*3 / ----- + --------- | 153*3 / ----- + --------- || | 153*3 / ----- + --------- | 153*3 / ----- + --------- || | 153*3 / ----- + --------- | \ \/ 15606 5202 \ \/ 15606 5202 // \ \/ 15606 5202 \ \/ 15606 5202 // \ \/ 15606 5202 /
$$\left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)\right) \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)\right) \left(- \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}\right)$$
=
256 --- 289
$$\frac{256}{289}$$
256/289
Respuesta numérica
[src]
x1 = 1.0
x2 = -0.970142608992334 + 0.02986446360174*i
x3 = -0.970142608992334 - 0.02986446360174*i
x4 = 0.940285217984668
x4 = 0.940285217984668