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Olá,
![x^{4}+ x^{2} -20=0\\
( x^{2} )^2+ x^{2} -20=0\\\\
x^{2} =k\\\\
k^2+k-20=0\\\\
k= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}= \dfrac{-1\pm \sqrt{1^2-4*1*(-20)} }{2*1}= \dfrac{-1\pm \sqrt{1+80} }{2}\\\\\\
k= \dfrac{-1\pm \sqrt{81} }{2}= \dfrac{-1\pm9}{2}~\to~\begin{cases}k'=4\\
k''=-5\end{cases}\\
x^{2} =k\\
x^{2} =4~~~~~~~~~~~~~~~~~~~~~~~~ x^{2} =-5~\notin~R\\
x=\pm \sqrt{4}\\
x=\pm2\\\\\\\
\boxed{S=\{2,-2\}}](https://tex.z-dn.net/?f=+x%5E%7B4%7D%2B+x%5E%7B2%7D+-20%3D0%5C%5C%0A%28+x%5E%7B2%7D+%29%5E2%2B+x%5E%7B2%7D+-20%3D0%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%5C%5C%0Ak%5E2%2Bk-20%3D0%5C%5C%5C%5C%0Ak%3D+%5Cdfrac%7B-b%5Cpm+%5Csqrt%7Bb%5E2-4ac%7D+%7D%7B2a%7D%3D+%5Cdfrac%7B-1%5Cpm+%5Csqrt%7B1%5E2-4%2A1%2A%28-20%29%7D+%7D%7B2%2A1%7D%3D+%5Cdfrac%7B-1%5Cpm+%5Csqrt%7B1%2B80%7D+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%0Ak%3D+%5Cdfrac%7B-1%5Cpm+%5Csqrt%7B81%7D+%7D%7B2%7D%3D+%5Cdfrac%7B-1%5Cpm9%7D%7B2%7D%7E%5Cto%7E%5Cbegin%7Bcases%7Dk%27%3D4%5C%5C%0Ak%27%27%3D-5%5Cend%7Bcases%7D%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%0A+x%5E%7B2%7D+%3D4%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E+x%5E%7B2%7D+%3D-5%7E%5Cnotin%7ER%5C%5C%0A+x%3D%5Cpm+%5Csqrt%7B4%7D%5C%5C%0Ax%3D%5Cpm2%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BS%3D%5C%7B2%2C-2%5C%7D%7D++ "x^{4}+ x^{2} -20=0\\
( x^{2} )^2+ x^{2} -20=0\\\\
x^{2} =k\\\\
k^2+k-20=0\\\\
k= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}= \dfrac{-1\pm \sqrt{1^2-4*1*(-20)} }{2*1}= \dfrac{-1\pm \sqrt{1+80} }{2}\\\\\\
k= \dfrac{-1\pm \sqrt{81} }{2}= \dfrac{-1\pm9}{2}~\to~\begin{cases}k'=4\\
k''=-5\end{cases}\\
x^{2} =k\\
x^{2} =4~~~~~~~~~~~~~~~~~~~~~~~~ x^{2} =-5~\notin~R\\
x=\pm \sqrt{4}\\
x=\pm2\\\\\\\
\boxed{S=\{2,-2\}}")
Espero ter ajudado e tenha ótimos estudos =))
Espero ter ajudado e tenha ótimos estudos =))
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