Question

当x=√3-√2时,求代数式x^4-9x^2+2√2+1 的值

Answer 1

5-2根号6+2根号2

x^4-9x^2+2√2+1

=(√3-√2)^4-9*(√3-√2)^2+2√2+1

=(5-2√6)^2-9*(5-2√6)+2√2+1

=49-20√6-45+18√6+2√2+1

=5-2√6+2√2