Question 80239: Number problems. Find two consecutive positive integers such that the sum of
their squares is 85.
thanks
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! :
"Find two consecutive positive integers"
x, (x+1)
:
"the sum of their squares is 85."
x^2 + (x+1)^2 = 85
:
FOIL (x+1)(x+1) and you have:
x^2 + x^2 + 2x + 1 = 85
:
Subtract 85 from both sides:
x^2 + x^2 + 2x + 1 - 85 = 0
:
Combine like terms:
2x^2 + 2x - 84 = 0
:
Simplify, divide equation by 2:
x^2 + x - 42 = 0
:
Easily factored to:
(x + 7)(x - 6) = 0
:
x = -7, x = +6, the positive integer is what we want here:
:
The two positive consecutive integers: 6, 7
:
:
Check solution: 6^2 + 7^2 = 85
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