document.write( "Question 416350: Solve by using a quadratic equation to find three consecutive integers such that the sum of their squares is 1877. \n" ); document.write( "

Algebra.Com's Answer #291706 by htmentor(1343) $\"\"$ $\"About$

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Let the consecutive integers be n, n+1, and n+2
\n" ); document.write( "We have $\"n%5E2+%2B+%28n%2B1%29%5E2+%2B%28n%2B2%29%5E2+=+1877\"$
\n" ); document.write( "Multiplying terms gives $\"n%5E2+%2B+n%5E2+%2B+2n+%2B+1+%2B+n%5E2+%2B+4n+%2B+4+=+1877\"$
\n" ); document.write( "Collecting like terms and putting in the proper form gives
\n" ); document.write( " $\"+3n%5E2+%2B+6n+-+1872+=+0+\"$
\n" ); document.write( "Applying the quadratic formula we get
\n" ); document.write( " $\"n+=+%28-6+%2B-+sqrt%286%5E2+-+4%2A3%2A%28-1872%29+%29%29%2F%282%2A3%29\"$ -> $\"%28-6+%2B-+150%29%2F6\"$
\n" ); document.write( "This gives n = -26, 24
\n" ); document.write( "So one set of consecutive integers is 24,25,26 and the other is -26,-25,-24
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