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Question

If the roots of the equation x2kx+m=0 is tan2x and cot2x, then the minimum possible value of k+m is

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Solution

Roots are tan2x and cot2x
We know that tan2x+cot2x=ba=k
Also, tan2xcot2x=ca=m
tan2xcot2x=1=m

tan2x+1tan2x=k
Let tan2x=X
X+1X=k
We know that the minimum value of X+1X is 2, where X>0
Minimum value of k+m is 2+1=3

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