Question

当x=根号3＋根号2分之根号3-根号2，y=根号3-根号2分之根号3＋根号2时，求代数式x的平方+y的平方-5xy的值

Answer 1

x=(√3+√2)/(√3-√2)=(√3+√2)²=5+2√6

y=(√3-√2)/(√3+√2)=(√3-√2)²=5-2√6

∴x²+y²-5xy

=x²+2xy+y²-7xy

=(x+y)²-7xy

=(5+2√6+5-2√6)²-7(5+2√6)(5-2√6)

=100-7(25-24)

=100-7

=93