Problem:
How many different real numbers x satisfy the equation
(x2−5)2=16?
Answer Choices:
A. 0
B. 1
C. 2
D. 4
E. 8
Solution:
Recall that a2−b2=(a+b)(a−b). We can do the following rearrangement:
(x2−5)2−42⇒(x2−5+4)(x2−5−4)⇒(x+1)(x−1)(x+3)(x−3)=0=0=0.
From this we can see that there are 4 possible values for x.
Thus, the correct answer is D.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions