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Learn MoreTry out this beautiful algebra problem from AMC 8, 2019 based on the Fundamental Theorem of Algebra

How many different real numbers satisfy the equation

Algebra

Value

Telescoping

But try the problem first...

Answer: is (D) 4

Source

AMC 8, 2019, Problem 20

1st Hint

The given equation is

and that means

2nd Hint

Among both cases, if

then,

and that means we have 2 different real numbers that satisfy the equation.

Final Step

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.

- https://www.cheenta.com/smallest-perimeter-of-triangle-aime-2015-question-11/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s

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