The number of solution of the equation |...

The number of solution of the equation `|tan^(-1)|x||=sqrt((x^(2)+1)^(2)-4x^(2))` is

A

2

B

3

C

4

D

none of these

Verified by Experts

The correct Answer is:

C

`sqrt((x^(2)+1)^(2)-4x^(2))=sqrt((x^(2)-1)^(2))=|x^(2)-1|`
`rArr |tan^(-1)|x||=|x^(2)-1|`
Draw the graphs of `y=|tan^(-1)|x||` and `y=|x^(2)-1|`

From the graph, it is clear that equation has four roots.

Similar Questions

Explore conceptually related problems

The number of solutions of the equation x^("log"sqrt(x)^(2x)) =4 is

The number of solutions of the equation x^(log_(sqrt(x))2x)=4

The number of real solution of the equation tan^(-1) sqrt(x^(2) - 3x + 2) + cos^(-1) sqrt(4x - x^(2) -3) = pi is

Number of solutions of the equations |2x^(2)+x-1|=|x^(2)+4x+1|

The number of real solution of the equation tan^(-1)sqrt(x^(2)-3x+7)+cos^(-1)sqrt(4x^(2)-x+3)=pi is

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

Number of solutions of the equation 4x^(2)e^(-x)-1=0

The number of solutions for the equation sin^(-1) sqrt((x^(2)-x+1))+cos^(-1)sqrt((x^(2)-x))=pi is :

The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(2) is 2(b)3 (c) 1(d)0