Q15 of 83 Page 90

The product of two consecutive even natural numbers is 224. Find the numbers.

Let two consecutive even natural numbers be x and x + 2.

⇒ x(x + 2) = 224


⇒ x2 + 2x – 224 = 0


⇒ x2 + (16 – 14)x – 224 = 0


⇒ x2 + 16x – 14x – 224 = 0


⇒ x(x + 16) – 14(x + 16) = 0


⇒ (x – 14)(x + 16) = 0


⇒ x = 14 or x = – 16


But x is a natural no.


⇒ x = 14 is the first natural no.


And, second no. = x + 2


= 16


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