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Question
Two number differ by 4 and their product is 192. Find the numbers?
Solution
Let two required numbers be x and (x + 4)
Then according to question
x(x + 4) = 192
x2 + 4x - 192 = 0
x2 + 16x - 12x - 192 = 0
x(x + 16) - 12(x + 16) = 0
(x + 16)(x - 12) = 0
x + 16 = 0
x = -16
Or
x - 12 = 0
x = 12
Since, x being a number,
Therefore,
When x = -16 then
x + 4 = -16 + 4 = -12
And when x = 12 then
x + 4 = 12 + 4 = 16
Thus, two consecutive number be either 12, 16 or -16, -12.
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