Question
If a, b, c are real numbers such that a + 2b + c = 4 then max. value of ab + bc + ca is
Answer: Option B
:
B
Given (a+b)+(b+c)=4
But [(a+b)+(b+c)2]2≥[(a+b)(b+c)],A.M≥G.M.
or (42)2≥ab+bc+ca+b2
4−b2≥∑ab or ∑ab≤4−b2
∴ Max. value of ∑ab=4⇒(b)
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:
B
Given (a+b)+(b+c)=4
But [(a+b)+(b+c)2]2≥[(a+b)(b+c)],A.M≥G.M.
or (42)2≥ab+bc+ca+b2
4−b2≥∑ab or ∑ab≤4−b2
∴ Max. value of ∑ab=4⇒(b)
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