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Find the minimum value of (a+b+c)(1/a+1/b+1/c)? This is a question from progressions ,Algebra.
Find the minimum value of (a+b+c)(1/a+1/b+1/c)?This is a question from progressions ,Algebra.


5 years ago

Anoopam Mishra
126 Points
							You must be knowing that $AM \geqslant GM$.$\frac{a+b+c}{3} \geqslant (abc)^{1/3}$ and $\frac{1}{3} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c} )\geqslant (\frac{1}{a} \frac{1}{b} \frac{1}{c})^{1/3}$Multiplying both these inequalities, we get$=> \frac{1}{9}(a+b+c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c} )\geqslant (abc)^{1/3} (\frac{1}{a} \frac{1}{b} \frac{1}{c})^{1/3}$$=> (a+b+c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c} )\geqslant 9$The minimum value of $(a+b+c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c} )$ is 9.

5 years ago
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### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions