Question

各位帮个忙啦，一个初中数学题

(10^n+25)^2-(10^n-25)^2=10^16，则n=___

Answer 1

平方差公式~~
n=14.
左边=[(10^n+25)+(10^n-25)][(10^n+25)-(10^n-25)]=100X10^n=10^(n+2)
所以：n=14

Answer 2

(10^n+25)^2-(10^n-25)^2=10^16
10^2n+50*10^n+25*25-(10^2n-50*10^2n+25*25)=
10^2n+50*10^n+25*25-10^2n+50*10^2n-25*25=
2*50*10^n=10^(2+n)=10^16
n=14

Answer 3

(10^n+25)^2-(10^n-25)^2=10^2n+50*10^n+25^2-10^2n+50*10^n-25^2=100*10^n=10^(2+n)=10^16
所以n=14