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AMC 8 2019 Problem 20 | Fundamental Theorem of Algebra

Try out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.

AMC 8 2019 Problem 20:

How many different real numbers <img loading=" width="10" height="8"> satisfy the equation<p class=     \[(x^{2}-5)^{2}=16?\]

" width="119" height="19">

\textbf{(A) }0
\textbf{(B) }1
\textbf{(C) }2
\textbf{(D) }4
\textbf{(E) }8

Key Concepts

Algebra

Value

Telescoping


Check the Answer


Answer: is (D) 4

AMC 8, 2019, Problem 20

Try with Hints


The given equation is

<img loading=" width="129" height="22"/>

and that means

<img loading=" width="125" height="20"/>

Among both cases, if

<img loading=" width="106" height="20"/>

then,

<img loading=" width="204" height="20"/>

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

and if we take another case, then

<img loading=" width="125" height="20"/>

and so,

<img loading=" width="203" height="20"/>

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.

Cheenta Numerates Program for AMC - AIME

Subscribe to Cheenta at Youtube


Try out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.

AMC 8 2019 Problem 20:

How many different real numbers <img loading=" width="10" height="8"> satisfy the equation<p class=     \[(x^{2}-5)^{2}=16?\]

" width="119" height="19">

\textbf{(A) }0
\textbf{(B) }1
\textbf{(C) }2
\textbf{(D) }4
\textbf{(E) }8

Key Concepts

Algebra

Value

Telescoping


Check the Answer


Answer: is (D) 4

AMC 8, 2019, Problem 20

Try with Hints


The given equation is

<img loading=" width="129" height="22"/>

and that means

<img loading=" width="125" height="20"/>

Among both cases, if

<img loading=" width="106" height="20"/>

then,

<img loading=" width="204" height="20"/>

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

and if we take another case, then

<img loading=" width="125" height="20"/>

and so,

<img loading=" width="203" height="20"/>

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.

Cheenta Numerates Program for AMC - AIME

Subscribe to Cheenta at Youtube


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