Question

um número elevado a quarta potência foi adicionado ao dobro do quadrado do mesmo número , que é igual a três​

Answer 1

$\large\boxed{\begin{array}{l}\rm x^4+2x^2=3\\\rm x^4+2x^2-3=0\\\rm (x^2)^2+2x^2-3=0\\\underline{\sf fac_{\!\!,}a}\\\rm x^2=y,com\,y\geqslant0\\\rm y^2+2y-3=0\\\rm\Delta=b^2-4ac\\\rm\Delta=2^2-4\cdot1\cdot(-3)\\\rm\Delta=4+12\\\rm\Delta=16\\\rm y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm y=\dfrac{-2\pm\sqsrt{16}}{2\cdot1}\\\\\rm y=\dfrac{-2\pm8}{2}\begin{cases}\rm y_1=\dfrac{-2+8}{2}=\dfrac{6}{2}=3\\\rm y_2=\dfrac{-2-8}{2}=-\dfrac{10}{2}=-5\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf voltando\!:}\\\rm para\,y=3\\\rm x^2=3\\\rm x=\pm\sqrt{3}\\\rm para\,y=-5\\\rm x^2=-5\\\rm \not\exists x\in\mathbb{R}\\\rm S=\{-\sqrt{3},\sqrt{3}\}\end{array}}$