Question

The product of two consecutive even integers is 32 less than the square of the greater integer. Find the smaller integer.

Answer 1

14

Explanation:

x = \dfrac{28}{4}

I.e x = 7

Now, pout the value of x in 1

So, The smallest even integer = 2 x = 2 × 7 = 14

1. Hence, The smallest even integer is 14 Answer

Answer 2

The smallest even integer is 14

Explanation:

Given as :

The product of two consecutive even integers is 32 less than the square of the greater integer.

Let the smallest even integer = 2 x ...........1

And The greatest even integer = 2 x + 2 ..........2

Now, According to question

smallest even integer × greatest even integer = (greatest even integer)² - 32

Or, (2 x + 2) × 2 x = (2 x + 2)² - 32

Or, 4 x² + 4 x = 4 x² + 8 x + 4 - 32

Or, (4 x² + 8 x) - (4 x² + 4 x) = 32 - 4

Or, (4 x²- 4 x²) + (8 x - 4 x) = 28

Or, 0 + 4 x = 28

∴ x =
`(28)/(4)`

I.e x = 7

Now, pout the value of x in 1

So, The smallest even integer = 2 x = 2 × 7 = 14

Hence, The smallest even integer is 14 Answer