Question

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

Answer 1

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

Answer 2

Answer:

The exact value of a ⋅ b is:

                          13

Step-by-step explanation:

The equation in terms of the variable x is given by:

$2(x+4)^2=6$

On diving both side of the equation by 2 we get:

$(x+4)^2=3$

Also,

$(x+4)=\pm \sqrt{3}$

( Since, on taking square root on both the sides of the equation)

Hence, we get:

$x=-4\pm \sqrt{3}$

i.e.

$x=-4+\sqrt{3}$

and

$x=-4-\sqrt{3}$

i.e.

$a=-4+\sqrt{3}\ and\ b=-4-\sqrt{3}$

Hence,

$a.b=(-4+\sqrt{3})(-4-\sqrt{3})\\\\i.e.\\\\a.b=(-4)^2-(\sqrt{3})^2\\\\i.e.\\\\a.b=16-3\\\\i.e.\\\\a.b=13$