SOLUTION: Find the two consecutive positive integer such that the sum of their squares is 145.
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Question 697461: Find the two consecutive positive integer such that the sum of their squares is 145.
Found 3 solutions by Alan3354, stanbon, Positive_EV:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the two consecutive positive integer such that the sum of their squares is 145.
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8 & 9
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the two consecutive positive integer such that the sum of their squares is 145.
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1st: x
2nd: x+1
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Equation:
x^2 + (x+1)^2 = 145
x^2 + x^2 + 2x + 1 = 145
2x^2 + 2x - 144 = 0
x^2 + x - 72 = 0
Factor:
(x+9)(x-8) = 0
Positive solution:
x = 8
x+1 = 9
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Cheers,
Stan H.
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
Call the smaller of the two integers x. The larger integer is one higher, so it equals x+1. We are told the sum of their squares is 145, so:
, simplifying yields:
, giving a quadratic equation. Set one side equal to 0:
, simplfy by dividing both sides by 2:
, which can be factored as
(x-8)(x+9) = 0, so x = 8 or -9. Since you are looking for positive integers, x = 8 is the smaller number, and the larger number is 8 + 1 = 9. A quick check:
.
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