If a>0, b>0, c>0 and the minimum value of a(b2+c2)+b(c2+a2)+c(a2+b2) is λabc ,then λ is
A
2
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B
1
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C
6
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D
3
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Solution
The correct option is C 6 Taking the numbers ab2 and ac2 ab2+ac22≥√ab2.ac2 ⇒ab2+ac2≥2abc ________(1) Similarly, bc2+ba2≥2abc _______(2) and ca2+cb2≥2abc ________(3) Adding (1),(2) and (3) a(b2+c2)+b(c2+a2)+c(a2+b2)≥6abc Hence, option C is correct