已知m²+2mn=13,3mn+2n²=21,求2m²+13mn+6n²-44的值.
问题描述:
已知m²+2mn=13,3mn+2n²=21,求2m²+13mn+6n²-44的值.
答
m²+2mn=13,则2(m²+2mn)=26,即2m²+4mn=26
3mn+2n²=21,则3(3mn+2n²)=63,即9mn+6n²=63
(2m²+4mn)+(9mn+6n²)=26+63
2m²+13mn+6n²=89
2m²+13mn+6n²-44=89-44=45
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