Question

Determine whether the conjecture is true or false. If false, give a counterexample.

Given: x2+4=8
Conjecture: x=−2

Answer 1

I think it is False, x=2

Answer 2

We start with the given equation

`x^(2) + 4 = 8`

Now, we solve the equation, we subtract 4 on either side,

`x^(2) +4 -4 = 8-4`

`x^(2) = 4`

`x = √(4)`

`√(4 ) = +2 and -2`

x = +2 or -2

So, x= +2 and x =-2

Since the given conjuncture says X=-2, we can conclude that the given conjuncture is TRUE