The-number-of-solutions-of-the-equation-cos-pi-x-4-cos-pi-x-1-is-

Question Number 17148 by Tinkutara last updated on 01/Jul/17

The number of solutions of the equation

\cos (π \sqrt{x - 4}) \cos (π \sqrt{x}) = 1 is

Answered by ajfour last updated on 01/Jul/17

\Rightarrow \cos (π \sqrt{x - 4}) = \pm 1

and \cos (π \sqrt{x}) = \pm 1

which means for n, k \in + ve integers

π \sqrt{x - 4} = n π and π \sqrt{x} = k π

both n, k simultaneously

odd or even (including zero);

\Rightarrow x - 4 = n^{2} and x = k^{2}

combining them we have :

n^{2} + 4 = k^{2}

\Rightarrow n = 0, k = 2

and none other . .

x = k^{2} = 4

hence x = 4 seems to be the

only solution .

Commented by Tinkutara last updated on 01/Jul/17

Thanks Sir!