Question : What is the difference of the factors of the expression $x^2+\frac{1}{x^2}-6$?
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 4
Answer (1)
25th Jan, 2024
Correct Answer: 4
Solution :
$x^2+\frac{1}{x^2}-6$
= $x^2+\frac{1}{x^2}-2-4$
= $x^2+\frac{1}{x^2}-2×x^2×\frac{1}{x^2}-(2)^2$
= $(x-\frac{1}{x}^2)-(2)^2$
= $(x-\frac{1}{x}+2)(x-\frac{1}{x}-2)$
These are the two factors.
So, the difference between them is $(x-\frac{1}{x}+2-x+\frac{1}{x}+2)=4$
Hence, the correct answer is 4.
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