CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The number of real solutions of the equation

cos(ex) = 2+ 2-x is

(a) 0          (b) 1         (c) 2        (d) infinitely many


Solution

we all know exponential function is always positive 
here , 2⁻ˣ and 2ˣ both are exponential function. so, both are positive.
       we also know, all positive term follow 
AM≥ GM
so, 
(2⁻ˣ + 2ˣ)/2 ≥√(2⁻ˣ.2ˣ)


(2⁻ˣ + 2ˣ) ≥ 2

hence cos(eˣ) = (2⁻ˣ + 2ˣ) ≥2 

but we know  maximum value of  cos function is 1 
hence cos(eˣ) ≠ 2 

hence no any solution is possible here.
no of solution = 0

 

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image