The minimum value of a-b-c1-a-1-b-1-c for a-0- b-0 and c-0 is

Since, A.M≥ H.M ∴a+b+c3≥31a+1b+1c ⇒(a+b+c)(1a+1b+1c)≥9 ...

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Relation between AM,GM,HM for 2 Numbers

The minimum v...

Question

The minimum value of $(a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$ for $a > 0, b > 0$ and $c > 0$ is

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(a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})

a > 0, b > 0

c > 0

0 < a, b, c < 1

a + b + c = 2

\frac{a}{1 - a} \times \frac{b}{1 - b} \times \frac{c}{1 - c}

> 0

(a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) \geq 9

a > 0, b > 0, c > 0

a (b^{2} + c^{2}) + b (c^{2} + a^{2}) + c (a^{2} + b^{2})

λ a b c

λ

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a + b + c}

(a + b + c) \neq 0

a b c \neq 0

(a + b) (b + c) (c + a) ?

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