Question

Решите уравнение:

х^4 - 10〖 х〗^2 + 9 = 0

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Answer 1

$x^{4}-10x^{2}+9=0\\\\x^{2}=m, \ m\geq0\\\\m^{2}-10m+9=0\\\\D=(-10)^{2} -4*9=100-36=64=8^{2} \\\\m_{1} =\frac{10-8}{2}=1\\\\m_{2}=\frac{10+8}{2}=9\\\\1)x^{2}=1\\\\x_{1} =1\\\\x_{2}=-1\\\\2)x^{2}=9\\\\x_{3}=3\\\\x_{4}=-3\\\\Otvet:\boxed{1; \ -1; \ 3; \ -3}$