Try out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.
How many different real numbers 
satisfy the equation![\[(x^{2}-5)^{2}=16?\]](https://latex.artofproblemsolving.com/d/1/8/d188c4697f3f7cf1889796a037bd60b6dae3b29e.png)
$\textbf{(A) }0$
$\textbf{(B) }1$
$\textbf{(C) }2$
$\textbf{(D) }4$
$\textbf{(E) }8$
Algebra
Value
Telescoping
Answer: is (D) 4
AMC 8, 2019, Problem 20
The given equation is
and that means
Among both cases, if
then,
and that means we have 2 different real numbers that satisfy the equation.
and if we take another case, then
and so,
and that means we have 2 different real numbers in this `case too that satisfy the equation. So total 2+2=4 real numbers that satisfy the equation.
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