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1 solution
Moderator note:
Can you explain it clearly?
What is
?
How did you reach that claim and why is it true?
The minimum value of expression of the form k(x^2) + l(y^2) + z^2 is t*2^(1/2) where t is a root of the expression 2(t^2)-(2k+2l+1)t+2kl=0 and t<min(k,l) & also iff xy+yz+zx=1 Similarly here also in our question xy+yz+zx=1 so we apply the formula to get the answer. As xy+yz+zx=1 so to find the minimum value of the expression we need to use AM-GM inequality repeatedly t(x^2)+1/2(z^2)>((2t)^1/2)xz t(y^2)+1/2(z^2)>((2t)^1/2)yz (k-t)(x^2)+(l-t)(y^2)>2{(k-t)(l-t)}^(1/2)xy Then we equate ((2t)^1/2) & 2{(k-t)(l-t)^1/2} WE get the above mentioned equation on t x denotes tanA, y denotes tanB, z denotes tanC...