[latex]x^{10}-31x^{5}-32=0[/latex] 2) [latex]x^{4}-12x^{2}+27=0[/latex] 3) [latex]x^{8}-82x^{4}+81=0[/latex]

1. [latex]\\x^{10}-31x^{5}-32=0\\ x^{10}+x^5-32x^5-32=0\\ x^5(x^5+1)-32(x^5+1)=0\\ (x^5-32)(x^5+1)=0\\ x^5-32=0 \vee x^5+1=0\\ x^5=32 \vee x^5=-1\\ x=2 \vee x=-1[/latex] 2. [latex]\\x^{4}-12x^{2}+27=0\\ x^4-3x^2-9x^2+27=0\\ x^2(x^2-3)-9(x^2-3)=0\\ (x^2-9)(x^2-3)=0\\ (x-3)(x+3)(x^2-3)=0\\ x=3 \vee x=-3 \vee x=-\sqrt{3} \vee x=\sqrt3 [/latex] 3. [latex]\\x^{8}-82x^{4}+81=0\\ x^8-x^4-81x^4+81=0\\ x^4(x^4-1)-81(x^4-1)=0\\ (x^4-81)(x^4-1)=0\\ (x^2-9)(x^2+9)(x^2-1)(x^2+1)=0\\ (x-3)(x+3)(x^2+9)(x-1)(x+1)(x^2+1)=0\\ x=3 \vee x=-3 \vee x=1 \vee x=-1[/latex]