Question

What are the solutions of the equation 2x2 = 2? Use a graph of the related function. A. There are two solutions: -1 and 1. B. There are two solutions: -1 and 1. C. There are two solutions: D. There are no real number solutions.

Answer 1

hello :
2x² = 2
x²=1
x²-1=0
(x-1)(x+1) = 0
x-1=0 or x+1=0
x=1 or x= -1...(answer : B. There are two solutions: -1 and 1 )

Answer 2

There are two solutions : -1 and 1.

Explanation:

We are given equation in terms of variable x as:

`2x^2=2`

On dividing both side of the equation by 2 we get the equation as:

`x^2=1`

This could also be written as:

`x^2-1=0`

which is further written as:

`(x-1)(x+1)=0`

( Since, we have:

`a^2-b^2=(a-b)(a+b)` )

Hence, we have:

`x=1\ and\ x=-1`

Hence, the graph of this equation ( i.e.
`x^2-1=0` )will be point of intersection of:

`y=x^2-1` and
`y=0`