SOLUTION: Divide 12 into two parts such that the sum of their squares is 74. We need to find the two numbers.

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Question 513646: Divide 12 into two parts such that the sum of their squares is 74. We need to find the two numbers.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = one of the numbers
Then the other number = 12 - x
Sum of the squares is 74:
x^2 + (12-x)^2 = 74
Solve for x:
x^2 + 144 - 24x + x^2 = 74
2x^2 - 24x + 70 = 0
x^2 - 12x + 35 = 0
Factor:
(x-7)(x-5) = 0
So the numbers are 5 and 7