sin(x)^3+cos(x)^3=sin(x)^2+cos(x)^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
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x3 = - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 //
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
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x4 = - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
$$x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
x4 = -2*re(atan(1 + sqrt(2)*i)) - 2*i*im(atan(1 + sqrt(2)*i))
Suma y producto de raíces
[src]
pi / / ___\\ / / ___\\ / / ___\\ / / ___\\
-- + - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 // + - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
2
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) + \left(\frac{\pi}{2} + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right)\right)$$
pi / / ___\\ / / ___\\ / / ___\\ / / ___\\
-- - 2*re\atan\1 + I*\/ 2 // - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 //
2
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + \frac{\pi}{2} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
pi / / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
0*--*\- 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 ///*\- 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 ///
2
$$0 \frac{\pi}{2} \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
$$0$$