document.write( "Question 697461: Find the two consecutive positive integer such that the sum of their squares is 145. \n" ); document.write( "

Algebra.Com's Answer #430036 by Positive_EV(69) $\"\"$ $\"About$

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Call the smaller of the two integers x. The larger integer is one higher, so it equals x+1. We are told the sum of their squares is 145, so:
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+%28x%2B1%29%5E2+=+145\"$ , simplifying yields:
\n" ); document.write( " $\"x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+145\"$ , giving a quadratic equation. Set one side equal to 0:
\n" ); document.write( " $\"2%2Ax%5E2+%2B+2x+%2B+1+=+145\"$
\n" ); document.write( " $\"2%2Ax%5E2+%2B+2x+-144+=+0\"$ , simplfy by dividing both sides by 2:
\n" ); document.write( " $\"x%5E2+%2B+x+-+72+=+0\"$ , which can be factored as
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\n" ); document.write( "\n" ); document.write( "(x-8)(x+9) = 0, so x = 8 or -9. Since you are looking for positive integers, x = 8 is the smaller number, and the larger number is 8 + 1 = 9. A quick check:
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\n" ); document.write( "\n" ); document.write( " $\"8%5E2+%2B+9%5E2+=+64+%2B+81+=+145\"$ .
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