if a0 ,b0 ,c0 and the maximum value of a(b 2 +c 2 ) +b(c 2 +a 2 ) +c(a 2 +b 2 ) is X abc ,then X is (a) 2 (b) 1 (c)6 (d) 3

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if a>0 ,b>0 ,c>0 and the maximum value of a(b 2 +c 2 ) +b(c 2 +a 2 ) +c(a 2 +b 2 ) is X abc ,then X is (a) 2 (b) 1 (c)6 (d) 3

Vikas TU · Answer

For Maximum value, of a(b 2 +c 2 ) +b(c 2 +a 2 ) +c(a 2 +b 2 ) every term needs to be maximum. = > that is considering a b c be triangle sides with a as hypotenuse for maximum for a(b 2 +c 2 ) b hypotenuse for b(c 2 +a 2 ) and c hypotenuse for c(a 2 +b 2 ). Thus from pythogorus for every term a^2 = b^2 + c^2 simlarly for last two term. put it in the eqn. U would get a^3 + b^3 + c^3 = 3abc X = 3 from the identity.

mycroft holmes · Answer

From AM-GM inequality with equality when b=c. Repeat this for the other two terms and add and you will get RHS with equality when a=b=c

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if a>0 ,b>0 ,c>0 and the maximum value of a(b 2 +c 2 ) +b(c 2 +a 2 ) +c(a 2 +b 2 ) is X abc ,then X is (a) 2 (b) 1 (c)6 (d) 3

if a>0 ,b>0 ,c>0 and the maximum value of a(b²+c²) +b(c²+a²) +c(a²+b²) is Xabc ,then X is (a) 2 (b) 1 (c)6 (d) 3

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if a>0 ,b>0 ,c>0 and the maximum value of a(b 2 +c 2 ) +b(c 2 +a 2 ) +c(a 2 +b 2 ) is X abc ,then X is (a) 2 (b) 1 (c)6 (d) 3

if a>0 ,b>0 ,c>0 and the maximum value of a(b2+c2) +b(c2+a2) +c(a2+b2) is Xabc ,then X is (a) 2 (b) 1 (c)6 (d) 3

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if a>0 ,b>0 ,c>0 and the maximum value of a(b²+c²) +b(c²+a²) +c(a²+b²) is Xabc ,then X is (a) 2 (b) 1 (c)6 (d) 3