WAEC - Mathematics (2015 - No. 11)
Adding 42 to a given positive number gives the same result as squaring the number. Find the number
14
13
7
6
Explanation
Let the given positive number be x
Then x + 42 = \(x^2\)
0 = \(x^2\) - x - 42
or \(x^2\) - x - 42 = 0
\(x^2\) - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
= (x + 6)(x - 7) = 0
x = -6 or x = 7
Hence, x = 7
Then x + 42 = \(x^2\)
0 = \(x^2\) - x - 42
or \(x^2\) - x - 42 = 0
\(x^2\) - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
= (x + 6)(x - 7) = 0
x = -6 or x = 7
Hence, x = 7
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