Q-the-equation-cos-4x-m-cos-2x-has-no-solution-x-0-pi-2-find-the-acceptable-real-values-for-m-

Question Number 191512 by mnjuly1970 last updated on 25/Apr/23

Q : t h e e q u a t i o n

⌊ \cos (4 x) ⌋ = m . \cos (2 x)

h a s n o s o l u t i o n . x \in (0, \frac{π}{2})

f i n d t h e a c c e p t a b l e

r e a l v a l u e s f o r^{″} m^{″} .

Answered by mahdipoor last updated on 26/Apr/23

[c o s (4 x)] = 0, 1, - 1 \overset{n o a n s w e r}{\Rightarrow} m c o s (2 x) \neq 0, 1, - 1

m \neq \frac{0, 1, - 1}{c o s (2 x)} \overset{1 < c o s x < - 1}{\Rightarrow} m \neq 0, R - (- 1, - 1)

\Rightarrow\Rightarrow m = [- 1, 1]