(10^n+25)^2-(10^n-25)^2=10^16,则n=___

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(10^n+25)^2-(10^n-25)^2=10^16,则n=___(10^n+25)^2-(10^n-25)^2=10^16,则n=___(10^n+25)^2-(10^n-25)^2=10^1

(10^n+25)^2-(10^n-25)^2=10^16,则n=___
(10^n+25)^2-(10^n-25)^2=10^16,则n=___

(10^n+25)^2-(10^n-25)^2=10^16,则n=___
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

(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

(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