Question

If α and β are roots of the equation x² + 5|x| – 6 = 0, then the value of |tan^–1α – tan^–1 β| is ______.

विकल्प

• `π/2`

• 0

• π

• `π/4`

Answer 1

If α and β are roots of the equation x² + 5|x| – 6 = 0, then the value of |tan^–1α – tan^–1 β| is `underlinebb(π/2)`.

Explanation:

It is given that, α and β are the roots of the equation

x² + 5|x| – 6 = 0

Here, |x|² + 6|x| – |x| – 6 = 0

`\implies` |x|(|x| + 6) – 1(|x| + 6) = 0

`\implies` (|x| + 6)(|x| – 1) = 0

|x| = –6, 1

As, modulus is always positive.

Therefore, |x| = 1 `\implies` x = ±1

Consider, α = 1 and β = –1

Hence, |tan^–1α – tan^–1 β|  = |tan^–11 – tan^–1 (–1)| 

= `|π/4 - (-π/4)|`

= `|π/2|`