document.write( "Question 565388: PLEASE SHOW ME HOW DID YOU GET THE ANSWER TO THIS - 1) The sum of two numbers is 18. And the sum of their squares is 170. Find the numbers \n" ); document.write( "

Algebra.Com's Answer #365776 by josmiceli(19441) $\"\"$ $\"About$

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Call numbers $\"+a+\"$ and $\"+b+\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+18+\"$
\n" ); document.write( "(2) $\"+a%5E2+%2B+b%5E2+=+170+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "(1) $\"+b+=+18+-+a+\"$
\n" ); document.write( "Substitute this into (2)
\n" ); document.write( "(2) $\"+a%5E2+%2B+%28+18+-+a+%29%5E2+=+170+\"$
\n" ); document.write( "(2) $\"+a%5E2+%2B+18%5E2+-+36a+%2B+a%5E2+=+170+\"$
\n" ); document.write( "(2) $\"+2a%5E2+-+36a+%2B+18%5E2+-+170+=+0+\"$
\n" ); document.write( "(2) $\"+2a%5E2+-+36a+%2B+324+-+170+=+0+\"$
\n" ); document.write( "(2) $\"+2a%5E2+-+36a+%2B+154+=+0+\"$
\n" ); document.write( "(2) $\"+a%5E2+-+18a+%2B+77+=+0+\"$
\n" ); document.write( "(2) $\"+a%5E2+-+18a+=+-77+\"$
\n" ); document.write( "complete the square
\n" ); document.write( "(2) $\"+a%5E2+-+18a+%2B+%2818%2F2%29%5E2+=+-77+%2B+%2818%2F2%29%5E2+\"$
\n" ); document.write( "(2) $\"+a%5E2+-+18a+%2B+81+=+-77+%2B+81+\"$
\n" ); document.write( "(2) $\"+%28+a+-+9+%29%5E2+=+2%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "(2) $\"+a+-+9+=+2+\"$
\n" ); document.write( "(2) $\"+a+=+11+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+b+=+18+-+a+\"$
\n" ); document.write( "(1) $\"+b+-+18+-+11+\"$
\n" ); document.write( "(1) $\"+b+=+7+\"$
\n" ); document.write( "The numbers are 11 and 7
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+a%5E2+%2B+b%5E2+=+170+\"$
\n" ); document.write( "(2) $\"+11%5E2+%2B+7%5E2+=+170+\"$
\n" ); document.write( "(2) $\"+121+%2B+49+=+170+\"$
\n" ); document.write( "(2) $\"+170+=+170+\"$
\n" ); document.write( "OK \n" ); document.write( "

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