document.write( "Question 769223: one positive integer is 6 less than twice a number. the sum of their squares is 164. find the integers \n" ); document.write( "

Algebra.Com's Answer #468700 by Jc0110(165) $\"\"$ $\"About$

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Let the positive integer to be x whereas the number to be y.
\n" ); document.write( " $\"x=2y-6\"$ ---> Equation 1 ... Substitute into Equation 2
\n" ); document.write( " $\"x%5E2%2By%5E2=164\"$ ---> Equation 2
\n" ); document.write( "____________________________________________________________
\n" ); document.write( " $\"%282y-6%29%5E2%2By%5E2=164\"$
\n" ); document.write( " $\"%284y%5E2-24y%2B36%29%2By%5E2=164\"$
\n" ); document.write( " $\"4y%5E2-24y%2B36%2By%5E2=164\"$
\n" ); document.write( " $\"4y%5E2%2By%5E2-24y%2B36-164=0\"$
\n" ); document.write( " $\"5y%5E2-24y-128=0\"$
\n" ); document.write( " $\"%285y%2B16%29%28y-8%29=0\"$
\n" ); document.write( " $\"y=-16%2F5\"$ or $\"y=8\"$
\n" ); document.write( "____________________________________________________________
\n" ); document.write( "If $\"y=-16%2F5\"$ , $\"x=2%28-16%2F5%29-6=-12%262%2F5\"$
\n" ); document.write( "* $\"x=-12%262%2F5\"$ is not the answer as x must be a positive integer.
\n" ); document.write( "If $\"y=8\"$ , $\"x=2%288%29-6=10\"$
\n" ); document.write( "* $\"x=10\"$ is the answer as x is a positive integer.
\n" ); document.write( "Thus, the integer is 10. \n" ); document.write( "

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