Quantitative Aptitude – Equation – The number of real-valued solutions of the equation

Slot – 1 – Quantitative Aptitude – Equation – The number of real-valued solutions of the equation

Q. The number of real-valued solutions of the equation 2^x + 2^-x = 2 – (x-2)^2 is?

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

Answer: 0

Solutions:
2^x +(1/2^x) =2-(x-2)^2
LHS:
2^x=positive value
2^x +(1/2^x)> =2
RHS:
(x-2)^2>=0 (square of a no. is always positive)
So 2-(x-2)^2<=2
So only possible solution will be when LHS =RHS that is when both of them are equal to 2
2 =2-(x-2)^2 [x=2]
Putting x=2 in LHS
2^2 + (1/2^2) = 4+1/4 [Not =2]
Therefore this Equation has no solution.

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