CAT 2019 Question Paper (Slot 1) Question 85

Question 85

The number of the real roots of the equation $$2 \cos (x(x + 1)) = 2^x + 2^{-x}$$ is

Solution

$$2 \cos (x(x + 1)) = 2^x + 2^{-x}$$

The maximum value of LHS is 2 when $$\cos (x(x + 1))$$ is 1 and the minimum value of RHS is 2 using AM $$\geq$$ GM 

Hence LHS and RHS can only be equal when both sides are 2. For LHS, cosx(x+1)=1   => x(x+1)=0   => x=0,-1

For RHS minimum value, x=0

Hence only one solution x=0


View Video Solution


Create a FREE account and get:

  • All Quant CAT Formulas and shortcuts PDF
  • 30+ CAT previous papers with solutions PDF
  • Top 500 CAT Solved Questions for Free

Comments

Register with

OR
cracku

Boost your Prep!

Download App