Question

Solve the equation (x-9)^6-13(x-9)^3+42=0

Answer 1

$(x-9)^6-13(x-9)^3+42=0\\t=(x-9)^3\\\\t^2-13t+42=0\\t^2-6t-7t+42=0\\t(t-6)-7(t-6)=0\\(t-7)(t-6)=0\\t=7 \vee t=6\\\\(x-9)^3=7 \vee (x-9)^3=6\\x-9=\sqrt[3]7 \vee x-9=\sqrt[3]6\\\boxed{x=9-\sqrt[3]7 \vee x=9+\sqrt[3]6}$