Find the number of solution(s) of the equation
`cos (pi sqrt(x)) cos (pi sqrt(x-4))=1`.

Options

A. more than 2
B. 2
C. 1
D. 0

Answer

C

Explanation

Given equation is meaningful for `x - 4 ge 0 " and" x ge 0 i.e. x ge 4`
Now, `"cos"(pi sqrt(x-4))"cos" (pi sqrt(x)) = 1`
`rArr "cos" (pi sqrt(x-4))= 1 " and cos"(pi sqrt(x)) = 1`
`rArr sqrt(x-4) = 0, 2, 4, 6… " and " sqrt(x) = 0, 2, 4, 6.... `
`rArr x -4 =0 , 2, 4, 6... " and " sqrt(x) = 0, 2, 4, 6..`
`rArr x = 4, 8, 20, 40, ... " and " x = 0, 4, 16, 36..`
`rArr x = 4`