document.write( "Question 948636: Find three consecutive positive on integers such that the sum of the squares of the first and second integers is equal to the square of the third integer -7 \n" ); document.write( "
Algebra.Com's Answer #579040 by macston(5194)\"\" \"About 
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X=first integer; X+2= second integer; X+4=third integer
\n" ); document.write( "\"X%5E2%2B%28X%2B2%29%5E2=%28X%2B4%29%5E2\"
\n" ); document.write( "\"X%5E2%2BX%5E2%2B4X%2B4=X%5E2%2B8X%2B16\" Subtract x^2 from each side
\n" ); document.write( "\"X%5E2%2B4X%2B4=8X%2B16\" Subtract 8X from each side.
\n" ); document.write( "\"X%5E2-4X%2B4=16\" Subtract 16 from each side.
\n" ); document.write( "\"X%5E2-4X-12=0\"\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"aX%5E2%2BbX%2Bc=0\" (in our case \"1X%5E2%2B-4X%2B-12+=+0\") has the following solutons:
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\n" ); document.write( " \"X%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-12=64\".
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\n" ); document.write( " Discriminant d=64 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--4%2B-sqrt%28+64+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"X%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+6\"
\n" ); document.write( " \"X%5B2%5D+=+%28-%28-4%29-sqrt%28+64+%29%29%2F2%5C1+=+-2\"
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\n" ); document.write( " Quadratic expression \"1X%5E2%2B-4X%2B-12\" can be factored:
\n" ); document.write( " \"1X%5E2%2B-4X%2B-12+=+1%28X-6%29%2A%28X--2%29\"
\n" ); document.write( " Again, the answer is: 6, -2.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-12+%29\"

\n" ); document.write( "\n" ); document.write( "The positive answer is 6 ANSWER: The first integer is 6
\n" ); document.write( "Note if not restricted to positive integers, (-2,0,2) also work.
\n" ); document.write( "X+2=8 ANSWER 2: The second integer is 8
\n" ); document.write( "X+4=10 ANSWER 3: The third integer is 10
\n" ); document.write( "CHECK
\n" ); document.write( "Sum of the squares of the first two equal square of the third.
\n" ); document.write( "\"6%5E2%2B8%5E2=10%5E2\"
\n" ); document.write( "\"36%2B64=100\"
\n" ); document.write( "\"100=100\"
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