Question

Solve the following equations.
$(x^2-6x{)}^2-2(x-3{)}^2=81$

Answer 1

let $(x-3{)}^2=a$

therefore the equation can be written as

$(a-9{)}^2-2a=81$

that is equals to $a^2-20a=0$

implies $a=0,20$

$(x-3{)}^2=0,20$

therefore $x=0,3-{20}^{1/2}$, $3+{20}^{1/2}$