The set of real solution for |x| ^2 – |x| -2 = 0 is x=-2 or x=2.
What is the real solution?
There are two real solutions for x if the discriminant's value is positive, which means that the graph of the solution has two distinct x-intercepts. This is called as the real solution.
Computation:
|x| ^2 – |x| -2 = 0
This can also be written as (|x| +1)(|x| -2)
then,
(|x| +1)(|x| -2) = 0
|x| +1 = 0 or |x| -2 = 0 (Using Zero factor principle)
Now, no solution for |x| +1 = 0 as x∈R
For |x| +2 = 0,
x = 2 or x = -2
Therefore, the solution for |x| ^2—|x| -2 = 0 is x=-2 or x=2.
Learn more about the real solutions, refer to:
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