What is 2^{sqrt(x)}-2^{1-sqrt(x)}>= 1 ?

The solution to 2^{sqrt(x)}-2^{1-sqrt(x)}>= 1 is No Solution

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2^{sqrt(x)}-2^{1-sqrt(x)}>= 1

2^{x} - 2^{1 - x} \geq 1

No Solution

Solution steps

2^{x} - 2^{1 - x} \geq 1

Apply exponent rules

(2^{x})^{2} - 2 \geq 2^{x}

Let

u = 2^{x}

u^{2} - 2 \geq u

u^{2} - 2 \geq u : u \leq - 1 or u \geq 2

u \leq - 1 or u \geq 2

Substitute back

u = 2^{x}

2^{x} \leq - 1 or 2^{x} \geq 2

2^{x} \leq - 1 :

No Solution

2^{x} \geq 2 : x \geq 1

Combine the intervals

No Solution or No Solution

Merge Overlapping Intervals

No Solution for x \in R

No Solution

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What is 2^{sqrt(x)}-2^{1-sqrt(x)}>= 1 ?
The solution to 2^{sqrt(x)}-2^{1-sqrt(x)}>= 1 is No Solution