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Question
Two numbers differ by 3 and their product is 504. Find the number
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Solution
Let the two numbers be x and x - 3 given that x(x + 3) = 504
⇒ x2 + 3x - 504 = 0
⇒ x2 + 24x - 21x - 504 = 0
⇒ x(x + 24) - 21(x + 24) = 0
⇒ (x + 24)(x - 21) = 0
Therefore,
⇒ x + 24 = 0
⇒ x = -24
Or
⇒ x - 21 = 0
⇒ x = 21
Since, x being a number,
Therefore,
When x = -24 then
x + 3 = -24 + 3 = -21
And when x = 21 then
x + 3 = 21 + 3 = 24
Thus, two consecutive numbers be either 21, 24 or -21, -24.
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