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

The smallest even integer is 14

Step-by-step 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 =

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

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step-by-step explanation:

i believe the answer is c.