SOLUTION: If Anne is 4 years older than Marie and the sum of the squares of their ages is 40. what are their individual ages?

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Question 1187483: If Anne is 4 years older than Marie and the sum of the squares of their ages is 40. what are their individual ages?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If Anne is 4 years older than Marie and the sum of the squares of their ages is 40. what are their individual ages?
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2 & 6

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Solving by trial and error is far easier than a formal algebraic solution. Simply look for a way to break 40 into the sum of two perfect squares.

1+39? no
4+36? YES

The squares of their ages are 4 and 36; their ages are 2 and 6. 6 is 4 more than 2, so that solution works.

But probably a formal algebraic solution was wanted....

Let x = Marie's age
Then x+4 = Anne's age

The sum of the squares of their ages is 40:

x%5E2%2B%28x%2B4%29%5E2=40
x%5E2%2Bx%5E2%2B8x%2B16=40
2x%5E2%2B8x-24=0
x%5E2%2B4x-12=0
%28x%2B6%29%28x-2%29=0
x=-6 OR x=2

Obviously the negative solution for Marie's age makes no sense; so x=2.

ANSWERS: Marie's age = x = 2; Anne's age = x+4 = 6