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BITSAT2024MathematicsSequences and SeriesActual

If a 0, b 0, c 0 and a, b, c are distinct, then (a+b)(b+c)(c+a) is greater than

Options

  1. A2(a+b+c)
  2. B3(a+b+c)
  3. C6 a b c
  4. D8 a b c

Correct answer

D. 8 a b c

Step-by-step solution

We know that AM GM ...(i) Now, applying Eq. (i) in a and b a+b 2 a b ....(ii) applying Eq. (i) in b and c b+c 2 b c ....(iii) and applying Eq. (i) in c and a c+a 2 c a ....(iv) By E'qs. (ii), (iii) and (iv) array cc & (a+b)(b+c)(c+a) 8 a b c & (a+b)(b+c)(c+a) 8 a b c array

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