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) (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:
^2 =\ -\frac{1}{k}\ +\ \frac{9}{4k^2})
In order for 
to have two identical roots (or one root with a multiplicity of 2, if you prefer) then 
\ =\ 0)
or 
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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