Find 3 consecutive even num big ears where the product of the smaller two numbers is 52 less than the square of the largest number

Smallest consecutive number =  6

Second consecutive number = 8

Largest consecutive number  = 10

Step-by-step explanation:

Let us assume the first even number =  k

Then the next consecutive even number  (k +2)

And the third consecutive even number =  (k+2) + 2= k + 4

Now, Product of two smaller number =  k (k+2)

Also, the square of the largest number =

Now, according to the question:

Now, using ALGEBRAIC IDENTITY:

or, k = 6

Hence, the smallest consecutive number = k = 6

Second consecutive number = k + 2 = 6 + 2 = 8

Largest consecutive number = k + 4 = 6 + 4 = 10

Hence, 6 , 8 and 10 are the required numbers.

69

step-by-step explanation: