Question 21894
 4^27+4^1000+4^x = (a perfect square number), what is x ?

 *** This does not belong to linear algebra.

 {{{4^27+4^1000+4^x =2^54 + 2^2000+ 2^(2x) =(2^x + 2^1000)^2, }}}

so {{{2*2^(x+1000)=2^54, or 2^(x+1001) = 2^54}}}. 

 We have x = 54-1001 = -947.

 Kenny