Let x = a and x = b be distinct solutions to the equation shown below. What is the exact value of a ⋅ b?

2 (x + 4) ^2 = 6

We have the following expression:

2 (x + 4) ^ 2 = 6

Let's clear the value of x:

x + 4 = + / - root (6/2)

x + 4 = + / - root (3)

x = + / - root (3) - 4

The solutions are:

a = root (3) - 4

b = - raiz (3) - 4

Multiplying both solutions we have:

a. b = (root (3) - 4) * ( - root (3) - 4)

a. b = - 9 - 4raiz (3) + 4raiz (3) + 16

a. b = - 9 + 16

a. b = 7

Answer:

the exact value of a ⋅ b is 7