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Question
Find two consecutive positive even integers such that their product is 1520.
Solution
Let the first integer be x.
So, the second integer would be x + 2.
Product of the two numbers = x(x + 2)
According to the question,
⇒ x(x + 2) = 1520
⇒ x2 + 2x = 1520
⇒ x2 + 2x – 1520 = 0
⇒ x2 + (40 – 38)x – 1520 = 0
⇒ x2 + 40x – 38x – 1520 = 0
⇒ x(x + 40) – 38(x + 40) = 0
⇒ (x – 38) (x + 40) = 0
⇒ x – 38 = 0 or x + 40 = 0
⇒ x = 38 or x = – 40
Because the numbers to be discovered are positive even integers
∴ x = 38
The first number = 38
The second number = 38 + 2 = 40
Therefore, 38 and 40 are needed as the numbers.
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