Question 287567
So you have a right triangle with sides x and x+2 and hypotenuse sqrt(6). By the Pythagorean Theorem:

x^2 + (x+2)^2 = (sqrt(6))^2

x^2 + x^2 + 4x + 4 = 6

2x^2 + 4x - 2 = 0

Divide both sides by 2:

x^2 + 2x - 1 = 0

Use the quadratic formula to find x and calculate x+2.