document.write( "Question 269817: solve by quadratic equation. Find 3 positive consecutive integers such that the sum of their squares is 245 \n" ); document.write( "

Algebra.Com's Answer #197668 by drk(1908) $\"\"$ $\"About$

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Let x, x+1 and x + 2 be 3 positive consecutive integers.
\n" ); document.write( "we get
\n" ); document.write( "(i) $\"x%5E2+%2B+%28x%2B1%29%5E2%2B+%28x%2B2%29%5E2+=+245\"$
\n" ); document.write( "expanding, we get
\n" ); document.write( "(ii) $\"x%5E2++%2B+x%5E2+%2B+2x+%2B+1+%2B+x%5E2+%2B+4x+%2B+4+=+245\"$
\n" ); document.write( "combine like terms to get
\n" ); document.write( "(iii) $\"3x%5E2+%2B+6x+%2B+5+=+245\"$
\n" ); document.write( "set = 0 to get
\n" ); document.write( "(iv) $\"3x%5E2+%2B+6x+-+240+=+0\"$
\n" ); document.write( "factoring, we get
\n" ); document.write( "(v) $\"%28x%2B10%29%283x-24%29+=+0\"$
\n" ); document.write( "and solving for x, we get
\n" ); document.write( "x = -10
\n" ); document.write( "or
\n" ); document.write( "x = 8.
\n" ); document.write( "The three numbers are 8, 9, and 10. \n" ); document.write( "

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