Quantitative Aptitude – Algebra – Functions

Slot -1 – Quantitative Aptitude – Algebra – Functions – The number of the real roots of the equation

Q. The number of the real roots of the equation 2cos (x ( x + 1 ) ) = 2^x + 2^-x is?

1. 1
2. 0
3. 2
4. infinite

Answer: 1

Solution: As we know maximum value of cos A = 1 at A =0
So maximum value of 2cos (x ( x + 1 ) ) = 2*1 =2
Minimum value of 2^x + 2^(-x) = 2 ( as the minimum value of k + 1/k = 2 at k = 1) at x = 0
Thus there is only one possible case when 2cos (x ( x + 1 ) ) = 2^x + 2^-x at x =0
So no of real solution =1

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