document.write( "Question 771731: A two-digit number has the property that the square of its tens digit plus ten times its units digit is equal to the square of its units digit plus ten times its ten digit. Find all two digit numbers which have this property, and are prime numbers. \n" ); document.write( "

Algebra.Com's Answer #470403 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = the tens digit
\n" ); document.write( "Let $\"+u+\"$ = the units digit
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+t%5E2+%2B+10u+=+u%5E2+%2B+10t+\"$
\n" ); document.write( " $\"+t%5E2+-+u%5E2+=+10t+-+10u+\"$
\n" ); document.write( " $\"+%28+t+-+u+%29%2A%28+t+%2B+u+%29+=+10%2A%28+t+-+u+%29+\"$
\n" ); document.write( "Divide both sides by $\"+t+-+u+\"$
\n" ); document.write( " $\"+t+%2B+u+=+10+\"$
\n" ); document.write( "The combinations where both digit
\n" ); document.write( "are prime are:
\n" ); document.write( "------------
\n" ); document.write( "t,u
\n" ); document.write( "---
\n" ); document.write( "1,9
\n" ); document.write( "9,1
\n" ); document.write( "7,3
\n" ); document.write( "3,7
\n" ); document.write( "5,5
\n" ); document.write( "----
\n" ); document.write( "check:
\n" ); document.write( "37
\n" ); document.write( " $\"+t%5E2+%2B+10u+=+u%5E2+%2B+10t+\"$
\n" ); document.write( " $\"+7%5E2+%2B+10%2A3+=+3%5E2+%2B+10%2A7+\"$
\n" ); document.write( " $\"+49+%2B+30+=+9+%2B+70+\"$
\n" ); document.write( " $\"+79+=+79+\"$
\n" ); document.write( "OK- you can check the others
\n" ); document.write( " \n" ); document.write( "

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