已知m+n=7,mn=-5,求(m-n)(n-m)+(2m-n)+(m-2n)的值.
问题描述:
已知m+n=7,mn=-5,求(m-n)(n-m)+(2m-n)+(m-2n)的值.
(m-n)(n-m)+(2m-n)(m-2n)
答
(m-n)(n-m)+(2m-n)(m-2n)=-(m-n)²+(2m²-mn-4mn+2n²)=-m²+2mn-n²+2m²-5mn+2n²=m²-3mn+n²=(m+n)²-5mn=49-5*(-5)=74