Question

Resolva em r, a seguinte equação biquadrada (x2 + 13) (x2 + 1) = 85.

Answer 1

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

Answer 2

Resposta:

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