已知xy+y^2=3,x^2+xy=-1/2,求2x^2+3xy+y^2的值.
问题描述:
已知xy+y^2=3,x^2+xy=-1/2,求2x^2+3xy+y^2的值.
答
把xy+y^2=3减去x^2+xy=-1/2,得x^2-y^2=-7/2
又因为xy=3-y^2
所以2x^2+3xy+y^=2x^2+3(3-y^2)+y^2
=2(x^2-y^2)+9
=2