If the sum of two numbers is 16 and their product is 63. Then the smaller number is ______?
- 10
- 7
- 8
- None of these
Explanation
Let's denote the two numbers as x and y, where x is the smaller number.
Given:
x + y = 16 ... (1)
xy = 63 ... (2)
From (1), y = 16 - x. Substituting into (2):
x(16 - x) = 63
16x - x² = 63
x² - 16x + 63 = 0
Factoring the quadratic equation:
(x - 7)(x - 9) = 0
x = 7 or x = 9
Since x is the smaller number, x = 7.
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