Let a, b and c be real numbers such that a+ 2b + c = 4 then the maximum value of ab + bc + ca is

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Solution

The correct option is D
4

Let ab + bc + ca = x

$\Rightarrow 2 b^{2} + 2 (c - 2) b - 4 c + c^{2} + x = 0 S i n c e b ϵ R, ∴ c^{2} - 4 c + 4 - c^{2} + 4 c - x \geq 0 S i n c e c ϵ R ∴ x \leq 4$

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Let a, b and c be real numbers such that a+ 2b + c = 4 then the maximum value of ab + bc + ca is

The correct option is D 4 Let ab + bc + ca = x ⇒2b2+2(c−2)b−4c+c2+x=0Since b ϵ R,∴c2−4c+4−c2+4c−x≥0Since c ϵ R∴ x≤4

The correct option is D
4

Let ab + bc + ca = x

$\Rightarrow 2 b^{2} + 2 (c - 2) b - 4 c + c^{2} + x = 0 S i n c e b ϵ R, ∴ c^{2} - 4 c + 4 - c^{2} + 4 c - x \geq 0 S i n c e c ϵ R ∴ x \leq 4$