Question 900731
<pre>{{{system( 16^x-16^y= 64512,4^x-4^y= 224) }}}

{{{16^x-16^y= 64512}}}, and since {{{16=4^2}}}

{{{(4^2)^x-(4^2)^y=64512}}}

{{{4^(2x)-4^(2y)=64512}}}

{{{(4^x)^2-(4^y)^2=64512}}}

{{{(4^x-4^y)(4^x+4^y)=64512}}}, and since {{{4^x-4^y= 224 }}}

{{{224(4^x+4^y)=64512}}}

{{{(4^x+4^y)=288}}}

Now we have the system:

{{{system(4^x+4^y=288,4^x-4^y= 224) }}}

Adding the two equations:

{{{2*4^x=512}}}

{{{4^x=256}}}

{{{4^x=4^4}}}

{{{x=4}}}

Substituting in {{{4^x-4^y= 224}}}

{{{4^4-4^y= 224}}}

{{{256-4^y=224}}}

{{{-4^y=-32}}}

{{{4^y=32}}}, since {{{2^2=4}}} and {{{2^5=32}}}

{{{(2^2)^y=2^5}}}

{{{2^(2y)=2^5}}}

{{{2y=5}}}

{{{y=5/2}}}

So {{{x+y=4+5/2=8/2+5/2=13/2=6&1/2}}}

Edwin</pre>