已知x=1+√2,y=1-√2,求x²-3xy+y²的值RT

已知x=1+√2,y=1-√2,求x²-3xy+y²的值RT
已知x=1+√2,y=1-√2,求x²-3xy+y²的值
RT

已知x=1+√2,y=1-√2,求x²-3xy+y²的值RT
x²-3xy+y²
=x²+2xy+y² -5xy
=(x+y)² -5xy
显然
x+y=2,而xy=1-2= -1
所以
x²-3xy+y²
=4 +5
= 9