Question

resolva a seguinte equação biquadrada: ( x elevado a 2 +13) (x elevado a 2+1)=85 ​

Answer 1

(x^2+13)(x^2+1)=85\\
x^4+x^2+13x^2+13=85\\
x^4+14x^2-72=0\\\\
(x^2)^2+14(x^2)-72=0\\\\x^2=y\\\\
y^2+14y-72=0\\\\
\Delta=14^2-4\cdot1\cdot(-72)\\
\Delta=196+288\\
\Delta=484\\\\
y= \dfrac{-14\pm \sqrt{484} }{2\cdot1}= \dfrac{-14\pm22}{2}\begin{cases}y_1= \dfrac{-14+22}{2}= \dfrac{8}{2}=4\\\\
y_2= \dfrac{-14-22}{2}= \dfrac{-36}{2}=-18\end{cases}\\\\\\
x^2=y:\\\\\\
x^2=4\\
x=\pm \sqrt{4}\\
x=\pm2\\\\
x^2=-18\\
x= \sqrt{-18}~~(\notin~\mathbb{R})\\\\\\
\huge\boxed{\text{S}=\{2,-2\} }

olha como ficaa, affs