如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值
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![如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值](/uploads/image/z/3706503-15-3.jpg?t=%E5%A6%82%E6%9E%9C%28x%5Em%2Fx%5E2n%29%5E3%2Fx%5Em-n%E4%B8%8E4x%5E2%E6%98%AF%E5%90%8C%E7%B1%BB%E9%A1%B9%2C%E4%B8%942m%2B5n%3D6%2C%E6%B1%824m%5E2-25n%5E2%E7%9A%84%E5%80%BC)
如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值
如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值
如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值
答
(x^m/x^2n)^3/x^(m-n)
=[x^(m-2n)]^3/x^(m-n)
=x^3(m-2n)/x^(m-n)
=x^(3m-6n-m+n)
=x^(2m-5n)
与4x^2是同类项
所以
2m-5n=2
2m+5n=6
解方程组
得
m=2
n=2/5
4m^2-25n^2
=4×4-25×4/25
=16-4
=12
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