document.write( "Question 484760: two positive numbers differ by 7 and the sum of their squares is 169. find the numbers.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #331618 by Tatiana_Stebko(1539) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x is the first number
\n" ); document.write( "Let y is the second number
\n" ); document.write( "two positive numbers differ by 7, so $\"x-y=7\"$
\n" ); document.write( "the sum of their squares is 169, so $\"x%5E2%2By%5E2=169\"$
\n" ); document.write( "The system of equations
\n" ); document.write( " $\"system%28x-y=7%2Cx%5E2%2By%5E2=169%29\"$
\n" ); document.write( "From the first equation $\"x=7%2By\"$ substitute into the second equation
\n" ); document.write( " $\"%287%2By%29%5E2%2By%5E2=169\"$
\n" ); document.write( " $\"49%2B14y%2By%5E2%2By%5E2-169=0\"$
\n" ); document.write( " $\"2y%5E2%2B14y-120=0\"$ divide by 2
\n" ); document.write( " $\"y%5E2%2B7y-60=0\"$
\n" ); document.write( " $\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"y+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-60%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"y+=+%28-7+%2B-+sqrt%28289+%29%29%2F2+\"$
\n" ); document.write( " $\"y+%5B1%5D=+%28-7+%2B17%29%2F2+=5\"$
\n" ); document.write( " $\"y+%5B2%5D=+%28-7+-17%29%2F2+=-12\"$
\n" ); document.write( "If $\"y%5B1%5D=5\"$ , then $\"x%5B1%5D=7%2B5=12\"$
\n" ); document.write( "If $\"y%5B2%5D=-12\"$ , then x[2]=7+(-12)=-5}}}
\n" ); document.write( "Answer 5 and 12, or -5 and -12 \n" ); document.write( "

\n" );