已知x=根号2+1,y=根号2-1,求x²+xy+y²的值
问题描述:
已知x=根号2+1,y=根号2-1,求x²+xy+y²的值
答
因为:x=√2+1、y=√2-1
则:x+y=(√2+1)+(√2-1)=2√2
xy=(√2+1)(√2-1)=(√2)²-1²=2-1=1
则:
x²+xy+y²
=(x²+2xy+y²)-xy
=(x+y)²-xy
=(2√2)²-1
=8-1
=7