Question: If a root of the equation $\tan^{- 1}\alpha + \tan^{- 1}\beta$ is 4, while the roots of the equati...

Question

If a root of the equation $\tan^{- 1}\alpha + \tan^{- 1}\beta$ is 4, while the roots of the equation $\pi/4$ are same, then the value of $\pi/2$ will be.

Answer 1

Solution

Put $x^{4} - 4x^{3} + 6x^{2} - 4x + 1 = 0$ in $8x^{3} - 14x^{2} + 7x - 1 = 0$ , we get $1,\frac{1}{2},\frac{1}{4}$

Now second equation $4x^{3} + 16x^{2} - 9x - 36 = 0$ have equal roots. Therefore $- 2,\frac{2}{3}, - \frac{2}{3}$ .

Question: If a root of the equation \(\tan^{- 1}\alpha + \tan^{- 1}\beta\) is 4, while the roots of the equati...

Solution