Question

Determine as raízes da equação biquadrada: x⁴+x²-12=0

Answer 1

Resposta:

Explicação passo-a-passo:

$x^{4} +x^{2}-12 = 0\\x^{2} *x^{2} + x^{2} -12=0\\\\x^{2} = y\\\\y*y+y-12 = 0\\y^{2} +y-12=0\\\\\\ d=b^{2} -4ac\\d=1^{2} -4*1*(-12)\\d= 1 + 48\\d = 49\\\\y = \frac{-b\frac{+}{-} \sqrt{d} }{2a} \\y = \frac{-1\frac{+}{-} \sqrt{49} }{2*1} \\y =\frac{-1 \frac{+}{-}7 }{2} \\\\y^{'} = \frac{-1+7}{2} =\frac{6}{2} =3\\y^{"} =\frac{-1-7}{2} =\frac{-8}{2}=-4\\ \\x^{2} =y\\x^{2} =3\\x=\frac{+}{-} \sqrt{3} \\\\x^{2} =y\\x^{2} =-4\\x=\frac{+}{-} \sqrt{-4}\\x=\frac{+}{-} \sqrt{4i^{2} } \\x=\frac{+}{-} 2i$