Q: There are two numbers whose sum is 15 and whose squares have a sum of 113. Determine the values of these numbers.

A 3, 2
B 7, 9
C 7, 8
D 7, 4

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Answer: C

Explanation:

Given:

x + (15 - x) = 15
x^2 + (15 - x)^2 = 113
Find:

x and (15 - x)
Substitute the first equation into the expression for (15 - x) to get:

x^2 + (15 - x)^2 = 113
x^2 + 225 + x^2 - 30x + x^2 = 113
3x^2 - 30x + 112 = 0
Factor the quadratic equation:

(x - 7)(x - 8) = 0
Solve for x:

x = 7 or x = 8
Therefore, the two numbers are x = 7 and (15 - x) = 8.

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Q: There are two numbers whose sum is 15 and whose squares have a sum of 113. Determine the values of these numbers.

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