document.write( "Question 259570: two numbers differ by 8 and the sum of their squares is 320. find the two numbers \n" ); document.write( "

Algebra.Com's Answer #191035 by drk(1908) $\"\"$ $\"About$

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Let X and Y be the numbers. We get
\n" ); document.write( "(i) $\"x-y+=+8\"$
\n" ); document.write( "(ii) $\"x%5E2%2By%5E2+=+320\"$
\n" ); document.write( "solve (i) for x to get
\n" ); document.write( "(iii) $\"x+=+8+%2B+y\"$
\n" ); document.write( "substitute (iii) into (ii) to get
\n" ); document.write( "(iv) $\"%288%2By%29%5E2+%2B+y%5E2+=+320\"$
\n" ); document.write( "expanding, we get
\n" ); document.write( "(v) $\"y%5E2+%2B+16y+%2B+64+%2B+y%5E2+=+320\"$
\n" ); document.write( "combine like terms to get
\n" ); document.write( "(vi) $\"2y%5E2+%2B+16y+%2B+64+=+320\"$
\n" ); document.write( "setting =0 and factoring, we get
\n" ); document.write( "(vii) $\"2y%5E2+%2B+16y+-256+=+0\"$
\n" ); document.write( "factored, we get
\n" ); document.write( "(viii) $\"%28y%2B16%29%28y-8%29=0\"$
\n" ); document.write( "solving for y, we get
\n" ); document.write( "y = -16 or y = 8.
\n" ); document.write( "So, we have (-8, -16) ; (16,8) \n" ); document.write( "

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