document.write( "Question 760846: Find the 2 digit number which has the square of the sum of its digits equal to the number obtained by reversing it digit? \n" ); document.write( "
Algebra.Com's Answer #462928 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
10a+b = a two digit number
\n" ); document.write( ":
\n" ); document.write( "write what it says:
\n" ); document.write( ":
\n" ); document.write( "\"A 2 digit number which has the square of the sum of its digits
\n" ); document.write( " equal to the number obtained by reversing it's digit?\"
\n" ); document.write( "(a+b)^2 = 10b + a
\n" ); document.write( "We have two unknown with only one equation
\n" ); document.write( "Assume a = 1, find b
\n" ); document.write( "(1+b)^2 = 10b + 1
\n" ); document.write( "1 + 2b + b^2 = 10b + 1
\n" ); document.write( ":
\n" ); document.write( "b^2 + 2b - 10b = 1 - 1
\n" ); document.write( "b^2 - 8b = 0
\n" ); document.write( "divide both sides by b
\n" ); document.write( "b - 8= 0
\n" ); document.write( "b = 8
\n" ); document.write( "then the number is 18; (9^2 = 81)
\n" ); document.write( ":
\n" ); document.write( "I don't think there is any other number, except perhaps 10
\n" ); document.write( "(1+0)^2 = 0 + 1
\n" ); document.write( " \n" ); document.write( "
\n" );