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Question
If the product of two consecutive even integers is 224, find the integers.
Solution
Let first even integer = 2x
then second even integer = 2x + 2
According to the condition,
2x × (2x + 2) = 224
⇒ 4x2 + 4x - 224 = 0
⇒ x2 + x - 56 = 0
⇒ x2 + 8x - 7x - 56 = 0
⇒ x(x + 8) -7(x + 8) = 0
⇒ (x + 8)(x - 7) = 0
Either x + 8 = 0,
then x = -8
∴ First even integer = 2 × (-8) = -16
and second even integer = -16 + 2 = -14
or
x - 7 = 0,
then x = 7
∴ First even integer = 2x = 2 × 7 = 14
and second even integer = 14 + 2 = 16.
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