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a/(1+a) +b/(1+b) +c/(1+c)=1 a,b,c are positive real nos P.T. abc abc is less than equal to 1/8
a/(1+a) +b/(1+b) +c/(1+c)=1a,b,c are positive real nosP.T.abcabc is less than equal to 1/8


4 years ago

jagdish singh singh
173 Points
							$\hspace{-0.7 cm}Let \frac{a}{1+a}=x\Rightarrow a = \frac{x}{1-x} Similarly \frac{b}{1+b} = y\Rightarrow b=\frac{y}{1-y} \\\\ Similarly \frac{c}{1+c}=z\Rightarrow c=\frac{z}{1-z} and given a,b,c>0\\\\ So 0

4 years ago
Yogesh Kumar
43 Points
								$a/(1+a)+b/(1+b)+c/(1+c)=1$ on simplifying it we get, 	$ab+bc+ca+2abc=1$ Now Using AM ≥ GM,	(ab+bc+ca+2abc)÷4≥((2)(abc)3)¼	(1/4)4≥2(abc)3	(1/512)1/3≥abc or abc≤1/8Hence Proved

3 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