document.write( "Question 1145557: When 125 is added to a number, it becomes a perfect square. When 176 is added to that same number, it also becomes a perfect square. What is the number? \n" ); document.write( "
Algebra.Com's Answer #766773 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
125+x=y^2
\n" ); document.write( "176+x=z^2
\n" ); document.write( "z^2-y^2=51
\n" ); document.write( "x=y^2-125
\n" ); document.write( "x=z^2-176
\n" ); document.write( "y^2-125=z^2-176
\n" ); document.write( "z^2-y^2=176-125
\n" ); document.write( "z^2-y^2-51\r
\n" ); document.write( "\n" ); document.write( "The 2 squares differ by 51\r
\n" ); document.write( "\n" ); document.write( "We can solve it logically and using trial and error.
\n" ); document.write( "13^2 169
\n" ); document.write( "so z^2 must be at 14
\n" ); document.write( "30^2 =900
\n" ); document.write( "29^2= 841
\n" ); document.write( "which differ by 59
\n" ); document.write( "so y^2 must be less 30 and more than 14
\n" ); document.write( "
\n" ); document.write( "30 900
\n" ); document.write( "29 841
\n" ); document.write( "30 ^2 -29^2=59
\n" ); document.write( "900 -841=59 too much
\n" ); document.write( "20^2-19^2=
\n" ); document.write( "400-361=39 too small
\n" ); document.write( "59-39=20
\n" ); document.write( "Let's try half way
\n" ); document.write( "26 676
\n" ); document.write( "25 625
\n" ); document.write( "676-625=51
\n" ); document.write( "so x=25 y =26
\n" ); document.write( "625-125=500
\n" ); document.write( "676-176=500
\n" ); document.write( "x=500\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );