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.
-----------
8 & 9
You can put this solution on YOUR website! Find the two consecutive positive integer such that the sum of their squares is 145.
---
1st: x
2nd: x+1
---
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
=============
Cheers,
Stan H.
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:
(
