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Find all real solutions to 2^x+x^2=2-(1)...

Find all real solutions to `2^x+x^2=2-(1)/(2^x)`.

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Verified by Experts

Given equation is `2^(x) + (1)/(2^(x)) = 2 - x^(2)`
Using A.M `ge` G.M., we have `2^(x) + (1)/(2^(x)) ge 2`
But `2 - x^(2) le 2`
So, given equation holds only if `2^(x) + (1)/(2^(x)) = 2 - x^(2) = 2`
Therefore, x = 0 is the only solution.
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