(x^2-7)^2-10(x^2-7)+9=0

[latex]( x^{2} -7)^2-10( x^{2} -7)+9=0[/latex] введем замену: [latex] x^{2} -7=t[/latex] [latex]t^2-10t+9=0[/latex] [latex]D=100-36=64[/latex] [latex]t_1=9[/latex] [latex]t_2=1[/latex] [latex] x^{2} -7=9[/latex]   или   [latex] x^{2} -7=1[/latex] [latex] x^{2} -16=0[/latex] или   [latex] x^{2} -8=0[/latex] [latex](x-4)(x+4)=0[/latex]  или [latex](x+2 \sqrt{2} )(x-2 \sqrt{2} )=0[/latex] [latex]x=4[/latex] или [latex]x=-4[/latex] или [latex]x=-2 \sqrt{2} [/latex] или [latex]x=2 \sqrt{2} [/latex] Ответ:  [latex]4;-4;2 \sqrt{2} ;-2 \sqrt{2} [/latex]

[latex]( x^{2} -7) ^{2} -10( x^{2} 7)+9=0\\ x^{2} -7=t\\ \\ t ^{2} -10t+9=0\\D=100-369=64 \\ \sqrt{D} =8 \\ t _{1} = \frac{10+8}{2} = \frac{18}{2} =9 \\ \\ t_{2} = \frac{10-8}{2} = \frac{2}{2} =1 \\ \\ x^{2} -7=9\\ x^{2} =9+7\\ x^{2} =16\\x=+-4 \\ \\ [/latex] [latex]x^{2} -7=1\\ x^{2} =1+7\\ x^{2} =8\\x=+- \sqrt{8} \\ \\ x=+-2 \sqrt{2} [/latex] [latex]Otviet: +-4;+-2 \sqrt{2} [/latex]