若m为正整数,且x的2m次方=3.求(3x的3m次方)的2次方-13(x的2次方)的2m次方的值

问题描述:

若m为正整数,且x的2m次方=3.求(3x的3m次方)的2次方-13(x的2次方)的2m次方的值

[3x^(3m)]^2-13[(x^2)^(2m)]
=9x^(6m)-13x^(4m)
=9[x^(2m)]^3-13[x^(2m)]^2
将已知条件x^(2m)=3代入上式得
原式=9×3^3-13×3^2
=9×27-13×9
=9×(27-13)
=9×14
=126