Question

dem A=(4laN • 10laN+1) totul la2

Answer 1

$5^{2n+1}\times4^{3n+2}+10^{2n+1}\times2^{4n+1}=$

$=5^{2n+1}\times(2^2)^{3n+2}+(5\times2)^{2n+1}\times2^{4n+1}=$

$=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{2n+1}\times2^{4n+1}=$

$=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{2n+1+4n+1}=$

$=5^{2n+1}\times2^{6n+4}+5^{2n+1}\times2^{6n+2}=$

$=5^{2n+1}\times2^{6n+2}\times(2^2+1)=$

$=5^{2n+1}\times2^{6n+2}\times5=$

$=5^{2n+2}\times2^{6n+2}=$

$=5^{2(n+1)}\times2^{2(3n+1)}=$

$=(5^{n+1}\times2^{3n+1})^2=$

$=(5^{n+1}\times2^{n+1}\times2^{2n})^2=$

$=((5\times2)^{n+1}\times4^n)^2=$

$=(4^n\times10^{n+1})^2$