2019 AMC 8 Problem 20

Attempt Problem 20 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

20.

How many different real numbers xx satisfy the equation
(x2−5)2=16? (x^2 - 5)^2 = 16?
00
11
22
44
88
Answer: D
Concepts:difference of squaresquadratic
Small hint:
Let x2−5x^2 - 5 be the quantity being squared
Big hint:
Solve x2−5=4x^2 - 5 = 4 and x2−5=−4x^2 - 5 = -4
Video solution:
Solution video thumbnail
Play video

Click to load, then click again to play

Written solution:
Recall that a2−b2=(a+b)(a−b).a^2 - b^2 = (a + b)(a - b). We can do the following rearrangement. (x2−5)2−42=0(x2−1)(x2−9)=0 \begin{aligned} (x^2 - 5)^2 - 4^2 &= 0 \\ (x^2 - 1)(x^2 - 9) &= 0 \end{aligned}
From this we can see that there are 44 possible values for x.x.
Thus, the correct answer is D.
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.