已知关于x,y的多项式xⁿ﹣¹y+(m-3)xyⁿ﹣²-mxⁿ﹣³+4x²yⁿ﹣⁴(m,n为常数,且n大于4的整数)(1)如果该多项式合并同类型后是五次三项式,求m,n的值
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![已知关于x,y的多项式xⁿ﹣¹y+(m-3)xyⁿ﹣²-mxⁿ﹣³+4x²yⁿ﹣⁴(m,n为常数,且n大于4的整数)(1)如果该多项式合并同类型后是五次三项式,求m,n的值](/uploads/image/z/12951786-66-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%85%B3%E4%BA%8Ex%2Cy%E7%9A%84%E5%A4%9A%E9%A1%B9%E5%BC%8Fx%26%238319%3B%EF%B9%A3%26%23185%3By%EF%BC%8B%28m%EF%BC%8D3%29xy%26%238319%3B%EF%B9%A3%26%23178%3B%EF%BC%8Dmx%26%238319%3B%EF%B9%A3%26%23179%3B%EF%BC%8B4x%26%23178%3By%26%238319%3B%EF%B9%A3%26%238308%3B%EF%BC%88m%2Cn%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E4%B8%94n%E5%A4%A7%E4%BA%8E4%E7%9A%84%E6%95%B4%E6%95%B0%EF%BC%89%EF%BC%881%EF%BC%89%E5%A6%82%E6%9E%9C%E8%AF%A5%E5%A4%9A%E9%A1%B9%E5%BC%8F%E5%90%88%E5%B9%B6%E5%90%8C%E7%B1%BB%E5%9E%8B%E5%90%8E%E6%98%AF%E4%BA%94%E6%AC%A1%E4%B8%89%E9%A1%B9%E5%BC%8F%2C%E6%B1%82m%2Cn%E7%9A%84%E5%80%BC)
已知关于x,y的多项式xⁿ﹣¹y+(m-3)xyⁿ﹣²-mxⁿ﹣³+4x²yⁿ﹣⁴(m,n为常数,且n大于4的整数)(1)如果该多项式合并同类型后是五次三项式,求m,n的值
已知关于x,y的多项式xⁿ﹣¹y+(m-3)xyⁿ﹣²-mxⁿ﹣³+4x²yⁿ﹣⁴(m,n为常数,且n大于4的整数)
(1)如果该多项式合并同类型后是五次三项式,求m,n的值
已知关于x,y的多项式xⁿ﹣¹y+(m-3)xyⁿ﹣²-mxⁿ﹣³+4x²yⁿ﹣⁴(m,n为常数,且n大于4的整数)(1)如果该多项式合并同类型后是五次三项式,求m,n的值
根据你所说的合并同类项后的结果是五次三项式:
可以先把最高次项提取出来,得到
xⁿ﹣¹(y-mx﹣²)+yⁿ﹣²[(m-3)x+4x²y﹣²]
要出现三项式,此时只能令m=3可得
xⁿ﹣¹(y-3x﹣²)+yⁿ﹣²4x²y﹣²
再展开令n=6可得五次最高项
结果:m=3,n=6