CAT 2020 Exam Shift 1 Solved Paper

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Question : 57 of 76

Marks: +1, -0

The number of real-valued solutions of the equation

2^{x}+2^{-x}=2-(x-2)^{2}

is

infinite
1
0
2

Solution:

2^{x}+2^{-x}=2-(x-2)^{2}

The minimum value of

2^{x}+2^{-x}

is 2 when

x=0

But

x=0 ; 2-(x-2)^{2}=-2

The maximum value of

2-(x-2)^{2}

is 2 when

x=2

But

x=2 \;\; 2^{x}+2^{-x}=\;{17}/{4}

Hence there is no value of

x, 2^{x}+2^{-x}=2-(x-2)^{2}

The number of solutions is 0

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