已知x=根号3减根号2分之根号3加根号2,则X的平方减去10X加4的值为

题目

已知x=根号3减根号2分之根号3加根号2,则X的平方减去10X加4的值为

答案

x=(√3+√2)/(√3-√2)=(√3+√2)²/[(√3-√2)(√3+√2)]=(√3+√2)²=5+2√6
x²-10x+4
=x²-10x+25-21
=(x-5)²-21
=(5+2√6-5)²-21
=(2√6)²-21
=24-21
=3