Question

已知2m-n=3,4m+3n=1, 求5n(2m-n)^2-2(n-2m)^3的值

式子

Answer 1

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

Answer 2

=5n(2m-n)²+2(2m-n)³
=(2m-n)²(5n+4m-2n)
=(2m-n)²(4m+3n)
=3²*1
=9

Answer 3

2m-n=3 (1)
4m+3n=1 （2）
（1）*2-（2）可解得n=-1
则所求=5*（-1）*（3)^2-2*（-3)^3=9