不解方程组2m-n=3和4m+3n=1求5n(2m-n)^-2(n-2m)^的值
问题描述：
不解方程组2m-n=3和4m+3n=1求5n(2m-n)^-2(n-2m)^的值
答
x^2m=3 => x^m = 3^(1/2)
y^3n=2 => y^n=2^(1/3)
(x^3m)^2+(y^n)^3-x^my^4nx^3my^5n
=x^6m + y^3n - x^my^4nx^3my^5n
= (x^m)^6 + (y^n)^3 - (x^m)(y^n)^4 * (x^m)^3 * (y^n)^5
= [3^(1/2)]^6 + [2^(1/3)]^3 - 3^(1/2)* [2^(1/3)]^4 * [3^(1/2)]^3 * [2^(1/3)]^5
=3^3 + 3 - 3^(1/2)* [2^(4/3)] * [3^(3/2)] * [2^(5/3)]
= 9 + 3 - 3^2 * 2^3
= 9+ 3-6*6
= -24
答
将（2m-n）看成整体,值为3
方程（2）-（1）x2得,5n=-5
由方程（1）两边同时乘以-1得,n-2m=-3
将以上所得的值带入5n(2m-n)^-2(n-2m)^中即得要求的值!