SOLUTION: Find two numbers whose difference is 5 and the difference of their squares is 65

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Question 516282: Find two numbers whose difference is 5 and the difference of their squares is 65
Answer by gc2000(22) About Me  (Show Source):
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x - y = 5
x^2 - y^2 = 65
x = 5 + y


using the given:
x = 5 + y
square both sides
x^2 = 25 + 10y + y^2
x^2 = 65 + y^2
65 + y^2 = 25 +10y +y^2


65 = 25 + 10y
40 = 10y
4 = y
y = 4


x - y = 5
x - (4) = 5
x = 9


check, does 9^2 - 4^2 = 65?
yes, 81 - 16 = 65


x = 4, y = 9