Equações Biquadradas:
Resolva as equações em R:
a)X^4-21X^2+98=0
B)X^4-20X^2+64=0
C)X^4+X^2-110=0
Por favor me ajudem!
Respostas
respondido por:
2
E aí mano,
![x^4-21x^2+98=0\\
(x^2)^2-21x^2+98=0\\\\
x^2=k\\\\
k^2-21k+98=0\\
k'=14~~e~~k''=7\\\\
x^{2} =k\\\\
x^{2} =14~~~~~~~~~~~~ x^{2} =7\\
x=\pm\sqrt{14}~~~~~~~~x=\pm \sqrt{7}\\\\
\boxed{S=\{ \sqrt{14},- \sqrt{14}, \sqrt{7},- \sqrt{7} \}} x^4-21x^2+98=0\\
(x^2)^2-21x^2+98=0\\\\
x^2=k\\\\
k^2-21k+98=0\\
k'=14~~e~~k''=7\\\\
x^{2} =k\\\\
x^{2} =14~~~~~~~~~~~~ x^{2} =7\\
x=\pm\sqrt{14}~~~~~~~~x=\pm \sqrt{7}\\\\
\boxed{S=\{ \sqrt{14},- \sqrt{14}, \sqrt{7},- \sqrt{7} \}}](https://tex.z-dn.net/?f=+x%5E4-21x%5E2%2B98%3D0%5C%5C%0A%28x%5E2%29%5E2-21x%5E2%2B98%3D0%5C%5C%5C%5C%0Ax%5E2%3Dk%5C%5C%5C%5C%0Ak%5E2-21k%2B98%3D0%5C%5C%0Ak%27%3D14%7E%7Ee%7E%7Ek%27%27%3D7%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3D14%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E+x%5E%7B2%7D+%3D7%5C%5C%0Ax%3D%5Cpm%5Csqrt%7B14%7D%7E%7E%7E%7E%7E%7E%7E%7Ex%3D%5Cpm+%5Csqrt%7B7%7D%5C%5C%5C%5C%0A%5Cboxed%7BS%3D%5C%7B+%5Csqrt%7B14%7D%2C-+%5Csqrt%7B14%7D%2C+%5Csqrt%7B7%7D%2C-+%5Csqrt%7B7%7D+%5C%7D%7D+++)
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![x^4-20x^2+64=0\\
(x^2)^2-20 x^{2} +64=0\\\\
x^{2} =k\\\\
k^2-20k+64=0\\
k'=4~~e~~k''=16\\\\
x^{2} =k\\
x^{2} =4~~~~~~~~~~~~~~ x^{2} ~=16\\
x=\pm \sqrt{4}~~~~~~~~~~~x=\pm \sqrt{16} \\
x=\pm2~~~~~~~~~~~~~~x=\pm4\\\\
\boxed{S=\{2,-2,4,-4\}} x^4-20x^2+64=0\\
(x^2)^2-20 x^{2} +64=0\\\\
x^{2} =k\\\\
k^2-20k+64=0\\
k'=4~~e~~k''=16\\\\
x^{2} =k\\
x^{2} =4~~~~~~~~~~~~~~ x^{2} ~=16\\
x=\pm \sqrt{4}~~~~~~~~~~~x=\pm \sqrt{16} \\
x=\pm2~~~~~~~~~~~~~~x=\pm4\\\\
\boxed{S=\{2,-2,4,-4\}}](https://tex.z-dn.net/?f=x%5E4-20x%5E2%2B64%3D0%5C%5C%0A%28x%5E2%29%5E2-20+x%5E%7B2%7D+%2B64%3D0%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%5C%5C%0Ak%5E2-20k%2B64%3D0%5C%5C%0Ak%27%3D4%7E%7Ee%7E%7Ek%27%27%3D16%5C%5C%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+x%5E%7B2%7D+%7E%3D16%5C%5C%0Ax%3D%5Cpm+%5Csqrt%7B4%7D%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7Ex%3D%5Cpm+%5Csqrt%7B16%7D+%5C%5C%0Ax%3D%5Cpm2%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7Ex%3D%5Cpm4%5C%5C%5C%5C%0A%5Cboxed%7BS%3D%5C%7B2%2C-2%2C4%2C-4%5C%7D%7D)
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![x^2+ x^{2} -110=0\\
(x^2)^2+ x^{2} -110=0\\\\
x^{2} =k\\\\
k^2+k-110=0\\
k'=10~~e~~(k''=-11~\notin~R)\\\\
x^{2} =k\\
x^{2} =10\\
x=\pm \sqrt{10}\\\\
\boxed{S=\{ \sqrt{10},- \sqrt{10}\}} x^2+ x^{2} -110=0\\
(x^2)^2+ x^{2} -110=0\\\\
x^{2} =k\\\\
k^2+k-110=0\\
k'=10~~e~~(k''=-11~\notin~R)\\\\
x^{2} =k\\
x^{2} =10\\
x=\pm \sqrt{10}\\\\
\boxed{S=\{ \sqrt{10},- \sqrt{10}\}}](https://tex.z-dn.net/?f=x%5E2%2B+x%5E%7B2%7D+-110%3D0%5C%5C%0A%28x%5E2%29%5E2%2B+x%5E%7B2%7D+-110%3D0%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%5C%5C%0Ak%5E2%2Bk-110%3D0%5C%5C%0Ak%27%3D10%7E%7Ee%7E%7E%28k%27%27%3D-11%7E%5Cnotin%7ER%29%5C%5C%5C%5C%0A+x%5E%7B2%7D+%3Dk%5C%5C%0A+x%5E%7B2%7D+%3D10%5C%5C%0Ax%3D%5Cpm+%5Csqrt%7B10%7D%5C%5C%5C%5C%0A%5Cboxed%7BS%3D%5C%7B+%5Csqrt%7B10%7D%2C-+%5Csqrt%7B10%7D%5C%7D%7D+++)
Espero ter ajudado e tenha ótimos estudos =))
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Espero ter ajudado e tenha ótimos estudos =))
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