SOLUTION: For what constants k does the equation k 2^x + 2^{-x} = 3 have only one real solution x?

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Question 773597: For what constants k does the equation k 2^x + 2^{-x} = 3 have only one real solution x?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Multiply by



Let , substitute, and put the resulting quadratic in standard form:



Start the process to complete the square:







In order for to have two identical roots (or one root with a multiplicity of 2, if you prefer) then





or

John

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