Question

Determine o conjunto soluçao das seguintes equações x⁴- 9x²+2=0

Answer 1

Resposta:

$x=\sqrt{\frac{9+\sqrt{73}}{2}},\:x=-\sqrt{\frac{9+\sqrt{73}}{2}},\:x=\sqrt{\frac{9-\sqrt{73}}{2}},\:x=-\sqrt{\frac{9-\sqrt{73}}{2}}$

Explicação passo-a-passo:

$x^4-9x^2+2=0\\\\\mathrm{Para\:}\quad a=1,\:b=-9,\:c=2:\quad u_{1,\:2}=\frac{-\left(-9\right)\pm \sqrt{\left(-9\right)^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}\\\\u=\frac{9+\sqrt{73}}{2},\:u=\frac{9-\sqrt{73}}{2}\\\\\\x^2=\frac{9+\sqrt{73}}{2}\\\\x=\sqrt{\frac{9+\sqrt{73}}{2}},\:x=-\sqrt{\frac{9+\sqrt{73}}{2}}\\\\\\x^2=\frac{9-\sqrt{73}}{2}\\\\x=\sqrt{\frac{9-\sqrt{73}}{2}},\:x=-\sqrt{\frac{9-\sqrt{73}}{2}}$