SOLUTION: David is 5 years older than his sister. If the sum of the squares of their ages is 193, find their ages.

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Question 1091695: David is 5 years older than his sister. If the sum of the squares of their ages is 193, find their ages.
Answer by htmentor(1343) About Me  (Show Source):
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Let D = David's age
Then his sister's age will be D-5
The sum of the squares is 193:
D^2 + (D-5)^2 - 193 = 0
2D^2 - 10D - 168 = 0
D^2 - 5D - 84 = 0
This factors as:
(D+7)(D-12) = 0
Take the positive solution, D = 12
So David is 12 and his sister is 7