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Expresiones idénticas
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- -x-8x-8+xx+16x=-7/8
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Expresiones semejantes
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- (-x-8)(x-8)-x(x+16)x=-7/8
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(-x-8)(x-8)+x(x+16)x=-7/8 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
(-x - 8)*(x - 8) + x*(x + 16)*x = -7/8
$$x x \left(x + 16\right) + \left(- x - 8\right) \left(x - 8\right) = - \frac{7}{8}$$
Respuesta rápida
[src]
________________________ / ________________________\
/ _________ | / _________ |
/ 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 |
3 / ----- + -------------- | ___ \/ 3 *3 / ----- + -------------- |
\/ 16 16 75 | 75*\/ 3 \/ 16 16 |
x1 = -5 + ----------------------------- + ------------------------------- + I*|- ------------------------------- + -----------------------------------|
6 ________________________ | ________________________ 6 |
/ _________ | / _________ |
/ 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 |
2*3 / ----- + -------------- | 2*3 / ----- + -------------- |
\/ 16 16 \ \/ 16 16 /
$$x_{1} = -5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6}\right)$$
________________________ / ________________________ \
/ _________ | / _________ |
/ 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 |
3 / ----- + -------------- | \/ 3 *3 / ----- + -------------- ___ |
\/ 16 16 75 | \/ 16 16 75*\/ 3 |
x2 = -5 + ----------------------------- + ------------------------------- + I*|- ----------------------------------- + -------------------------------|
6 ________________________ | 6 ________________________|
/ _________ | / _________ |
/ 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 |
2*3 / ----- + -------------- | 2*3 / ----- + -------------- |
\/ 16 16 \ \/ 16 16 /
$$x_{2} = -5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right)$$
________________________
/ _________
/ 68013 27*\/ 2345361
3 / ----- + --------------
75 \/ 16 16
x3 = -5 - ----------------------------- - -----------------------------
________________________ 3
/ _________
/ 68013 27*\/ 2345361
3 / ----- + --------------
\/ 16 16
$$x_{3} = - \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{3} - 5 - \frac{75}{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}$$
x3 = -(27*sqrt(2345361)/16 + 68013/16)^(1/3)/3 - 5 - 75/(27*sqrt(2345361)/16 + 68013/16)^(1/3)
Suma y producto de raíces
[src]
suma
________________________ / ________________________\ ________________________ / ________________________ \ ________________________
/ _________ | / _________ | / _________ | / _________ | / _________
/ 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361
3 / ----- + -------------- | ___ \/ 3 *3 / ----- + -------------- | 3 / ----- + -------------- | \/ 3 *3 / ----- + -------------- ___ | 3 / ----- + --------------
\/ 16 16 75 | 75*\/ 3 \/ 16 16 | \/ 16 16 75 | \/ 16 16 75*\/ 3 | 75 \/ 16 16
-5 + ----------------------------- + ------------------------------- + I*|- ------------------------------- + -----------------------------------| + -5 + ----------------------------- + ------------------------------- + I*|- ----------------------------------- + -------------------------------| + -5 - ----------------------------- - -----------------------------
6 ________________________ | ________________________ 6 | 6 ________________________ | 6 ________________________| ________________________ 3
/ _________ | / _________ | / _________ | / _________ | / _________
/ 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361
2*3 / ----- + -------------- | 2*3 / ----- + -------------- | 2*3 / ----- + -------------- | 2*3 / ----- + -------------- | 3 / ----- + --------------
\/ 16 16 \ \/ 16 16 / \/ 16 16 \ \/ 16 16 / \/ 16 16
$$\left(- \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{3} - 5 - \frac{75}{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right) + \left(\left(-5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right)\right) + \left(-5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6}\right)\right)\right)$$
=
/ ________________________\ / ________________________ \
| / _________ | | / _________ |
| ___ / 68013 27*\/ 2345361 | | ___ / 68013 27*\/ 2345361 |
| ___ \/ 3 *3 / ----- + -------------- | | \/ 3 *3 / ----- + -------------- ___ |
| 75*\/ 3 \/ 16 16 | | \/ 16 16 75*\/ 3 |
-15 + I*|- ------------------------------- + -----------------------------------| + I*|- ----------------------------------- + -------------------------------|
| ________________________ 6 | | 6 ________________________|
| / _________ | | / _________ |
| / 68013 27*\/ 2345361 | | / 68013 27*\/ 2345361 |
| 2*3 / ----- + -------------- | | 2*3 / ----- + -------------- |
\ \/ 16 16 / \ \/ 16 16 /
$$-15 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right) + i \left(- \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6}\right)$$
producto
/ ________________________ / ________________________\\ / ________________________ / ________________________ \\ / ________________________\ | / _________ | / _________ || | / _________ | / _________ || | / _________ | | / 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 || | / 68013 27*\/ 2345361 | ___ / 68013 27*\/ 2345361 || | / 68013 27*\/ 2345361 | | 3 / ----- + -------------- | ___ \/ 3 *3 / ----- + -------------- || | 3 / ----- + -------------- | \/ 3 *3 / ----- + -------------- ___ || | 3 / ----- + -------------- | | \/ 16 16 75 | 75*\/ 3 \/ 16 16 || | \/ 16 16 75 | \/ 16 16 75*\/ 3 || | 75 \/ 16 16 | |-5 + ----------------------------- + ------------------------------- + I*|- ------------------------------- + -----------------------------------||*|-5 + ----------------------------- + ------------------------------- + I*|- ----------------------------------- + -------------------------------||*|-5 - ----------------------------- - -----------------------------| | 6 ________________________ | ________________________ 6 || | 6 ________________________ | 6 ________________________|| | ________________________ 3 | | / _________ | / _________ || | / _________ | / _________ || | / _________ | | / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 || | / 68013 27*\/ 2345361 | / 68013 27*\/ 2345361 || | / 68013 27*\/ 2345361 | | 2*3 / ----- + -------------- | 2*3 / ----- + -------------- || | 2*3 / ----- + -------------- | 2*3 / ----- + -------------- || | 3 / ----- + -------------- | \ \/ 16 16 \ \/ 16 16 // \ \/ 16 16 \ \/ 16 16 // \ \/ 16 16 /
$$\left(-5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6}\right)\right) \left(-5 + \frac{75}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{6} + \frac{75 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}{3} - 5 - \frac{75}{\sqrt[3]{\frac{27 \sqrt{2345361}}{16} + \frac{68013}{16}}}\right)$$
=
-519/8
$$- \frac{519}{8}$$
-519/8
Respuesta numérica
[src]
x1 = -15.2779379729827
x2 = 0.13896898649135 + 2.05596856307673*i
x3 = 0.13896898649135 - 2.05596856307673*i
x3 = 0.13896898649135 - 2.05596856307673*i