Answer:
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
<u>Now, According to question</u>
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