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If a+2b+c=4,then what is the maximum value of ab+bc+ac?
If a+2b+c=4,then what is the maximum value of ab+bc+ac?


4 years ago

vinayak prabhu sd
23 Points
							First,c=4-a-2b......(1),thensubstute it in ab+bc+ca.........(2)now differentiate this equation 2 times first wrt a and then wrt b.now that you have two equations, solve them using linear equations in two variables and get values for a and b.since you got those answers after differentiating them, you have their greatest values. now get the value for c using eqn (1).now again substute all the values in (2) and you thus have its greatest value.

4 years ago
jagdish singh singh
173 Points
							$\hspace{-0.7 cm}Using (A+B)^2\geq 4AB and equality hold when A=B\\\\ So (a+b+b+c)^2\geq 4(a+b)(b+c)\\\\ So 4(ab+bc+ca+b^2)\leq (a+2b+c)^2=4^2=16\\\\ So ab+bc+ca\leq 4-b^2\leq 4\\\\ So \max(ab+bc+ca) = 4 when a=c=2 and b=0$

4 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