document.write( "Question 659755: Find three consecutive integers such that the product of the first two plus the product of the first and the third is 14. \n" ); document.write( "

Algebra.Com's Answer #410906 by ReadingBoosters(3246) $\"\"$ $\"About$

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x; (x+1); (x+2)
\n" ); document.write( "(x)(x+1) + (x)(x+2) = 14
\n" ); document.write( "Distribute the x
\n" ); document.write( "x^2 + x + x^2 + 2x = 14
\n" ); document.write( "Combine like terms
\n" ); document.write( "2x^2 + 3x = 14
\n" ); document.write( "Set equal to 0
\n" ); document.write( "2x^2 + 3x - 14 = 0
\n" ); document.write( "( + )( - ) signs determined by -14
\n" ); document.write( "common multiples of 14: 1,14; 2,7\r
\n" ); document.write( "\n" ); document.write( "(2x + 7)(x - 2)
\n" ); document.write( "check by FOIL: 2x^2 - 4x + 7x - 14, which is 2x^2 + 3x -14
\n" ); document.write( "2x+7=0, x = -7/2: won't work
\n" ); document.write( "x-2=0, x = 2: correct
\n" ); document.write( "x+1=3, x+2=4\r
\n" ); document.write( "\n" ); document.write( "Proof:
\n" ); document.write( "(2)(3)= 6
\n" ); document.write( "(2)(4) = 8
\n" ); document.write( "6+8=14\r
\n" ); document.write( "\n" ); document.write( "Answer: 2, 3, 4 \n" ); document.write( "

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