Question

1)Resolva a equação biquadrada.
-x^4+113.x²-3136=0

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{-x^4 + 113x^2 -3136 = 0}$

$\sf{y = x^2}$

$\sf{-y^2 + 113y -3136 = 0}$

$\sf{\Delta = b^2 - 4.a.c}$

$\sf{\Delta = (113)^2 - 4.(-1).(-3136)}$

$\sf{\Delta = 12.769 - 12.544}$

$\sf{\Delta = 225}$

$\sf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-113 \pm \sqrt{225}}{-2} \rightarrow \begin{cases}\sf{y' = \dfrac{-113 + 15}{-2} = \dfrac{98}{2} = 49}\\\\\sf{y'' = \dfrac{-113 - 15}{-2} = \dfrac{128}{2} = 64}\end{cases}}$

$\sf{x^2 = 49}$

$\sf{x = \pm\:\sqrt{49}}$

$\sf{x = \pm\:7}$

$\sf{x^2 = 64}$

$\sf{x = \pm\:\sqrt{64}}$

$\sf{x = \pm\:8}$

$\boxed{\boxed{\sf{S = \{7,-7,8,-8\}}}}$