The sum of the squares of two numbers is 100. One number is 2 more than the other. Find the larger number?
- 8
- 9
- 7
- None of these
Explanation
Let the smaller number be x.
The larger number is x + 2.
Given:
x² + (x + 2)² = 100
x² + x² + 4x + 4 = 100
2x² + 4x - 96 = 0
x² + 2x - 48 = 0
(x + 8)(x - 6) = 0
x = -8 or x = 6
If x = -8, larger number = -8 + 2 = -6
If x = 6, larger number = 6 + 2 = 8
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