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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.

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ghanami
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:

There are two solutions : -1 and 1.

Step-by-step explanation:

We are given equation in terms of variable  x as:

                  [tex]2x^2=2[/tex]

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

                  [tex]x^2=1[/tex]

This could also be written as:

                [tex]x^2-1=0[/tex]

which is further written as:

[tex](x-1)(x+1)=0[/tex]

( Since, we have:

           [tex]a^2-b^2=(a-b)(a+b)[/tex]    )

Hence, we have:

 [tex]x=1\ and\ x=-1[/tex]

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

  [tex]y=x^2-1[/tex] and [tex]y=0[/tex]

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