exponential equation

$Solve for $x$ in $2^x+2^{\frac{1}{x}}=4$.

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1
Ricky ·

Apply AM - GM inequality on the quantity in the RHS . In the GM part , again apply AM - GM on the power of 2 . You' ll find that LHS is always greater than or equal to RHS . Hence , the answer is -

x = 1 :) , because only for this " x " , equality holds .

One thing that is to be cleared is that " x " cannot be " -ve " , otherwise there will be no real roots .

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