若x＝√2＋1＝√2－1 求x²－y²分之x²-3xy=y²的值

题目

若x＝√2＋1＝√2－1 求x²－y²分之x²-3xy=y²的值

答案

x=√2＋1,y=√2－1
x²－y²
=(√2+1)^2-(√2-1)^2
=4√2
x²-3xy+y²
(x-y)^2-xy
=4-1
=3
(x²-y²)/(x²-3xy+y²)
=4√2/3