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The number of the real roots | Quantitative Aptitude – Algebra – Functions

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Algebra – Functions – The number of the real roots…

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot -1 - Question 5 - The number of the real roots...

Q. 5: 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

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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