document.write( "Question 57584: how do i find three consecutive intergers such that the sum of the squares is 77. \n" ); document.write( "

Algebra.Com's Answer #39298 by funmath(2933) $\"\"$ $\"About$

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how do i find three consecutive intergers such that the sum of the squares is 77.
\n" ); document.write( "Let the 1st integer=x
\n" ); document.write( "then the 2nd integer=x+1
\n" ); document.write( "then the third integer=x+1+1=x+2
\n" ); document.write( "Then the equation to solve is:
\n" ); document.write( " $\"x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=77\"$
\n" ); document.write( " $\"x%5E2%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B4x%2B4%29=77\"$
\n" ); document.write( " $\"x%5E2%2Bx%5E2%2Bx%5E2%2B2x%2B4x%2B1%2B4=77\"$
\n" ); document.write( " $\"3x%5E2%2B6x%2B5=77\"$
\n" ); document.write( " $\"3x%5E2%2B6x%2B5-77=0\"$
\n" ); document.write( " $\"3x%5E2%2B6x-72=0\"$
\n" ); document.write( " $\"3%28x%5E2%2B2x-24%29=0\"$
\n" ); document.write( " $\"%283%2F3%29%28x%5E2%2B2x-24%29=0%2F3\"$
\n" ); document.write( " $\"%28x%5E2%2B2x-24%29=0\"$
\n" ); document.write( " $\"%28x%2B6%29%28x-4%29=0\"$
\n" ); document.write( "x+6=0 and x-4=0
\n" ); document.write( "x+6-6=0-6 and x-4+4=0+4
\n" ); document.write( "x=-6 and x=4
\n" ); document.write( "There are two possible sets of integers: -6,-5,-4 and 4,5,6
\n" ); document.write( ":
\n" ); document.write( "Check by seeing if the sum of their squares is = to 77
\n" ); document.write( " $\"%28-6%29%5E2%2B%28-5%29%5E2%2B%28-4%29%5E2=77\"$
\n" ); document.write( " $\"36%2B25%2B16=77\"$
\n" ); document.write( "77=77 checks
\n" ); document.write( " $\"%284%29%5E2%2B%285%29%5E2%2B%286%29%5E2=77\"$
\n" ); document.write( " $\"16%2B25%2B36=77\"$
\n" ); document.write( " $\"77=77\"$ this checks too.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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