Question

已知2^m+3^n+5^p=7,2^(m-1)+3^n+5^(p+1)=11 求2^(m+1)+3^n+5^(p-1)的

Answer 1

2^(m-1)+3^n+5^(p+1)=11

2^m/2+3^n+5*5^p=11 (1)

2^m+3^n+5^p=7 (2)

(1)-(2)

-2^m/2+4*5^p=4

2^m=8(5^p-1)>0 5^p>1

2^m=8(5^p-1)代入(2)

3^n+9*5^p-8=7

3^n=15-9*5^p>0

5^p