SOLUTION: The sumof the squares of three consecutive positive integers is 77. Find the integers. The book gives a hint: if one integer is x, the next consecutive positive integer is x+1,

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Question 353429: The sumof the squares of three consecutive positive integers is 77. Find the integers.
The book gives a hint: if one integer is x, the next consecutive positive integer is x+1, and the third is x+2
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of three consecutive positive integers is 77. Find the integers.
The book gives a hint: if one integer is x, the next consecutive positive integer is x+1, and the third is x+2
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The "book" is correct, but you could just as well use, x-1,x,x+1
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Equation:
(x-1)^2 + x^2 + (x+1)^2 = 77
x^2 -2x + 1 + x^2 + x^2+2x+1 = 77
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3x^2 +2 = 77
3x^2 = 75
x^2 = 25
x = 5
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1st: x-1 = 4
2nd: x = 5
3rd: x+1 = 6
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Checking:
4^2 + 5^2 + 6^2
= 16 + 25 + 36
= 77
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Cheers,
Stan H.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=77,
x%5E2%2Bx%5E2%2B2%2Ax%2B1%2Bx%5E2%2B4%2Ax%2B4=77,
3%2Ax%5E2%2B6%2Ax%2B5+=+77,
3%2Ax%5E2%2B6%2Ax-72+=+0,
x%5E2%2B2%2Ax-24+=0, after dividing both sides by 3.
%28x%2B6%29%2A%28x-4%29=0,
This implies that x=-6 or x=4. We reject the -6 as a solution.
Therefore the three consecutive positive integers are 4, 5, 6.