Question

已知X^m=5,X^n=3,求X^2m-3n的值.

Answer 1

(1)X^2m-3n=X^2m/X^3n(同底数幂除法公式的逆用a^m/a^n=a^m-n)

=(X^m)^2/(X^n)^3(幂的乘方公式的逆用)

=25/9

(2)由已知得:32^n=2^5n=6

2^3m-10n=2^3m/2^10n=(2^m)^3/(2^5n)^2=27/36=3/4

(3)用换元法做：

设A=X^2+Y^2,则原方程转化为：A(A+1)=12

解得：A1=-4 A2=3

又因为X^2+Y^2>0,所以X^2+Y^2=3

（4）k=9