已知:实数a、b、x、y满足a+b=x+y=3,ax+by=7 求(a*a+b*b)xy+ab(x*x+y*y)如题

问题描述:

已知:实数a、b、x、y满足a+b=x+y=3,ax+by=7 求(a*a+b*b)xy+ab(x*x+y*y)
如题

9=(a+b)(x+y)=ax+by+ay+bx=7+ay+bx,故ay+bx=2.(a^2+b^2)xy+ab(x^2+y^2)=a^2xy+abx^2+b^2xy+aby^2=ax(ay+bx)+by(bx+ay)=2ax+2by=2*7=14