Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

If x+y+z=1 and 0 x, y, z 1 , then the maximum value of expression 27(x y+y z+z x-2 x y z) is equal to

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aligned & (1-2 x)(1-2 y)(1-2 z)=1-2 x+4 x y-8 x y z=4 x y-8 x y z-1 & x y-2 x y z= 1+(1-2 x)(1-2 y)(1-2 z) 4 & (1-2 x) 3 (1-2 x)(1-2 y)(1-2 z) ^ 1 / 3 & (1-2 x)(1-2 y)(1-2 z) 1 27 & x y+y z+z x-2 x y z 7 27 aligned Equality holds for x = y = z = 1 3 Maximum value = 7 27

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