Question

The number of integer solutions of equation \(2|x|(x^2+1)=5x^2\) is

Answer 1

The correct answer is 3.

Answer 2

Let |x| = k
\(2k(k^2+1)=5k^2\)
Either k = 0; or 2(k² + 1) = 5k
2k² – 5k + 2 = 0
2k² – 4k – k + 2 = 0
2k(k – 2) –1(k – 2) = 0
(2k – 1)(k – 2) = 0
k = 0.5 or k = 2
∴ k which is |x|, can take the values 0, 0.5 or 2
So, x can take the values 0, -0.5, 0.5, -2, 2
Since we are looking for integral solutions, x can only take the values 0, 0.5 or 2
So, there are only 3 integral solutions to \(2|x|(x^2+1)=5x^2\)