Question

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!

Answer 1

E aí mano,

$x^4-21x^2+98=0\\ (x^2)^2-21x^2+98=0\\\\ x^2=k\\\\ k^2-21k+98=0\\ k'=14~~e~~k''=7\\\\ x^{2} =k\\\\ x^{2} =14~~~~~~~~~~~~ x^{2} =7\\ x=\pm\sqrt{14}~~~~~~~~x=\pm \sqrt{7}\\\\ \boxed{S=\{ \sqrt{14},- \sqrt{14}, \sqrt{7},- \sqrt{7} \}}$

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$x^4-20x^2+64=0\\ (x^2)^2-20 x^{2} +64=0\\\\ x^{2} =k\\\\ k^2-20k+64=0\\ k'=4~~e~~k''=16\\\\ x^{2} =k\\ x^{2} =4~~~~~~~~~~~~~~ x^{2} ~=16\\ x=\pm \sqrt{4}~~~~~~~~~~~x=\pm \sqrt{16} \\ x=\pm2~~~~~~~~~~~~~~x=\pm4\\\\ \boxed{S=\{2,-2,4,-4\}}$

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$x^2+ x^{2} -110=0\\ (x^2)^2+ x^{2} -110=0\\\\ x^{2} =k\\\\ k^2+k-110=0\\ k'=10~~e~~(k''=-11~\notin~R)\\\\ x^{2} =k\\ x^{2} =10\\ x=\pm \sqrt{10}\\\\ \boxed{S=\{ \sqrt{10},- \sqrt{10}\}}$

Espero ter ajudado e tenha ótimos estudos =))