document.write( "Question 539168: the sum of two integers is 10 and the sum of their squares is 82. find the integers \n" ); document.write( "

Algebra.Com's Answer #353345 by josmiceli(19441) $\"\"$ $\"About$

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$\"+a+%2B+b+=+10+\"$
\n" ); document.write( " $\"+a%5E2+%2B+b%5E2+=+82+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+b+=+10+-+a+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+a%5E2+%2B+%28+10+-+a+%29%5E2+=+82+\"$
\n" ); document.write( " $\"+a%5E2+%2B+100+-+20a+%2B+a%5E2+=+82+\"$
\n" ); document.write( " $\"+2a%5E2+-+20a+%2B+100+=+82+\"$
\n" ); document.write( " $\"+2a%5E2+-+20a+%2B+18+=+0+\"$
\n" ); document.write( " $\"+a%5E2+-+10a+%2B+9+=+0+\"$
\n" ); document.write( "complete the square
\n" ); document.write( " $\"+a%5E2+-+10a+=+-9+\"$
\n" ); document.write( " $\"a%5E2+-+10a+%2B+%28-10%2F2%29%5E2+=+-9+%2B+%28-10%2F2%29%5E2+\"$
\n" ); document.write( " $\"+a%5E2+-+10a+%2B+25+=+16+\"$
\n" ); document.write( " $\"+%28+a+-+5+%29%5E2+=+4%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+a+-+5+=+4+\"$
\n" ); document.write( " $\"+a+=+9+\"$
\n" ); document.write( "It is also true that
\n" ); document.write( " $\"+a+-+5+=+-4+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( "If I say that $\"+a+=+9+\"$ , then
\n" ); document.write( " $\"+a+%2B+b+=+10+\"$
\n" ); document.write( " $\"+b+=+1+\"$
\n" ); document.write( "The integers are 9 and 1
\n" ); document.write( "check:
\n" ); document.write( " $\"+9%5E2+%2B+1%5E2+=+82+\"$
\n" ); document.write( " $\"+81+%2B+1+=+82+\"$
\n" ); document.write( " $\"+82+=+82+\"$
\n" ); document.write( "OK \n" ); document.write( "

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