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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Sequences and Series

BITSAT 2020 · Mathematics · Sequences and Series

If a > 0, b > 0, c > 0 and a, b, c are distinct, then (a+ b)...

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

Options

  1. A2(a+b+c)2(a+b+c)
  2. B3(a+b+c)3(a+b+c)
  3. C6abc6 \mathrm{abc}
  4. D8abc8 \mathrm{abc}

Correct answer

D. 8abc8 \mathrm{abc}

Step-by-step solution

AM>GM⇒a+b2>ab,b+c2>bc,c+a2>ca\mathrm{AM} > \mathrm{GM}\Rightarrow \frac{\mathrm{a}+\mathrm{b}}{2} > \sqrt{\mathrm{ab}}, \frac{\mathrm{b}+\mathrm{c}}{2} > \sqrt{\mathrm{bc}}, \frac{\mathrm{c}+\mathrm{a}}{2} > \sqrt{\mathrm{ca}} So, (a+b)(b+c)(c+a)>8abc(a+b)(b+c)(c+a) > 8 a b c
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