Question

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

Answer 1

Solution :

Let x , ( x + 2 ) are two consecutive

even numbers .

product of these numbers = 224

=> x( x + 2 ) = 224

=> x² + 2x - 224 = 0

=> x² +16x - 14x - 224 = 0

=> x( x + 16 ) - 14( x + 16 ) = 0

=> ( x + 16 )( x - 14 ) = 0

x + 16 = 0 or x - 14 = 0

x = -16 or x = 14

Therefore,

Requires numbers are ,

i ) if x = -16 ,

x + 2 = -16 + 2 = -14

ii ) if x = 14

x + 2 = = 14 + 2 = 16

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