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Question
If the product of two positive consecutive even integers is 288, find the integers.
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Solution
Let first positive even integer = 2x
then second even integer = 2x + 2
According to the condition,
2x × (2x + 2) = 288
⇒ 4x2 + 4x – 288 = 0
⇒ x2 + x – 72 = 0 ...(Dividing by 4)
⇒ x2 - 9x - 8x - 72 = 0
⇒ x(x + 9) -8(x + 9) = 0
⇒ (x + 9)(x - 8) = 0
(x + 9) = 0 or (x - 8) = 0
x = -9 or x = 8
∴ Value of x = 8 [since, -9 is not positive]
∴ First even integer = 2x
= 2 × 8
= 16
and second even integer
= 16 + 2
= 18
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