document.write( "Question 731033: The sum of two number is 17 and sum of their squares is 145. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #446967 by hoomanc(14) $\"\"$ $\"About$

You can put this solution on YOUR website!
1) $\"a%2Bb=17\"$ & 2) $\"a%5E2%2Bb%5E2=145\"$ \r
\n" ); document.write( "\n" ); document.write( "Try to make equation #(2) from equation #(1):\r
\n" ); document.write( "\n" ); document.write( "so, $\"a%2Bb=17\"$ >>> $\"%28a%2Bb%29%5E2=17%5E2\"$ >>> $\"%28a%5E2%2Bb%5E2%2B2ab%29=289\"$ >>> from eq. #(2) >>> $\"%28145%2B2ab%29=289\"$ >>> $\"%282ab%29=144\"$ >>> $\"%28ab%29=72\"$ \r
\n" ); document.write( "\n" ); document.write( "Now use these two new equations: (2) $\"a%2Bb=17\"$ (3) $\"%28ab%29=72\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a%2Bb=17\"$ >>> $\"b=17-a\"$ substitute in eq. #(3)\r
\n" ); document.write( "\n" ); document.write( " $\"%28ab%29=72\"$ >>> $\"%28a%2817-a%29%29=72\"$ >>> $\"a%5E2-17a%2B72=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28a-8%29%28a-9%29=0\"$ >>> \r
\n" ); document.write( "\n" ); document.write( "(1) $\"a=8\"$ >>> $\"b=9\"$ or the other way,
\n" ); document.write( "(2) $\"a=9\"$ >>> $\"b=8\"$
\n" ); document.write( " \n" ); document.write( "

\n" );