Discussion Forum

If $\alpha$ and $\beta$ are roots of the equation x² +5|x|-6=0, then the value of $|tan^{-1}\alpha-\tan^{-1}\beta|=$ is 

Answer:

Explanation:

Given $\alpha$ and $\beta$  be the roots of the equation

 x² +5|x|-6=0,

 Now   |x|² +5|x|-6=0

 |x|²+6|x|-|x|-6=0

                    [by factorisation]

|x|(|x|+6)-1(|x|+6)=0

(|x|+6)(|x|-1)=0

|x|=-6 or |x|=1

(since, modulus cannot be giving negative values)

$\therefore$   $|x|=1\Rightarrow x=\pm1$

So,   $\alpha$ =1 and $\beta$  =-1 $\therefore$    Now, |$\tan ^{-1} \alpha - \tan ^{-1} \beta$|=|$\tan ^{-1} 1 - \tan ^{-1} -1|$

= $|\frac{\pi}{4}-\left(-\frac{\pi}{4}\right)|=|\frac{\pi}{4}+\frac{\pi}{4}|=|\frac{\pi}{2}|$