Question

Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

Answer 1

Let n represent the interger l, the three consective intergers are represented by

`n`

`n + 2`

`n + 4`

The second one represent

`(n + 2) {}^(2) + 76 =( n + 4) {}^(2)`

Simplify both sides

`n {}^(2) + 4n + 4 + 76 = {n}^(2) + 8n + 16`

`{n}^(2) + 4n + 4 = {n}^(2) + 8n - 60`

`4n + 4 = 8n - 60`

`4n + 64= 8n`

`64= 4n`

`n = 16`

The intergers are 16,18,20