已知A=3m²—2n²+mn,B=5mn—6m²—9n²,且满足A—B+3C=0求多项式C
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![已知A=3m²—2n²+mn,B=5mn—6m²—9n²,且满足A—B+3C=0求多项式C](/uploads/image/z/6965870-14-0.jpg?t=%E5%B7%B2%E7%9F%A5A%3D3m%26%23178%3B%E2%80%942n%26%23178%3B%2Bmn%2CB%3D5mn%E2%80%946m%26%23178%3B%E2%80%949n%26%23178%3B%2C%E4%B8%94%E6%BB%A1%E8%B6%B3A%E2%80%94B%2B3C%3D0%E6%B1%82%E5%A4%9A%E9%A1%B9%E5%BC%8FC)
已知A=3m²—2n²+mn,B=5mn—6m²—9n²,且满足A—B+3C=0求多项式C
已知A=3m²—2n²+mn,B=5mn—6m²—9n²,且满足A—B+3C=0求多项式C
已知A=3m²—2n²+mn,B=5mn—6m²—9n²,且满足A—B+3C=0求多项式C
A—B+3C=0
∴C=(B-A)/3
=[(5mn—6m²—9n²)-(3m²—2n²+mn)]/3
=(5mn-6m²-9n²-3m²+2n²-mn)/3
=(4mn-9m²-7n²)/3
A-B = 9m² + 7n² - 4mn
3C与A-B互为相反数
所以3C = -9m² -7n² + 4mn
C=-3m² - 7/3n² + 4/3mn