设x²＋xy=3,xy＋y²＝2,求2x²－xy－3y²的值

题目

设x²＋xy=3,xy＋y²＝2,求2x²－xy－3y²的值

答案

2x²－xy－3y²
=2x²+2xy-2xy－xy－3y²
=2x²+2xy-3xy－3y²
=2(x²+xy)-3(xy+y²)
x²＋xy=3,xy＋y²＝2
带入
2*3-3*2=0