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

Options

A. One
B. Two
C. Zero
D. Infinite

Answer

C

Explanation

as `0 le sqrt(x^(2) - 3x + 2) lt oo`
so `0 le tan^(-1) sqrt(x^(2) - 3x + 2) lt x//pi "…." (i) `
and `0 le sqrt(4x - x^(2) - 3 ) lt oo`
so `0 le cos^(-1) sqrt(4x - x^(2) - 3 ) le pi//2 "….." ( ii)`
so from (i) + (ii)
`0 le tan^(-1) sqrt(x^(2) - 3x +2 ) cos^(-1) sqrt(4x-x^(2) - 3) lt pi`
so no solution