Question

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation

• A. 0 ≤ M ≤ 1
• B. 1 ≤ M ≤ 2
• C. 2 ≤ M ≤ 3
• D. 3 ≤ M ≤ 4

Answer 1

Answer: (D)

3 ≤ M ≤ 4

Answer 2

3 ≤ M ≤ 4

As A.M. ≥ G.M. for positive real numbers, we get

$\frac { ( \mathrm { a } + \mathrm { b } ) + ( \mathrm { c } + \mathrm { d } ) } { 2 } \geq \sqrt { ( \mathrm { a } + \mathrm { b } ) ( \mathrm { c } + \mathrm { d } ) }$ ⇒ M ≤ I

(Putting values)

Also(a + b) (c + d) > 0

[^..^. a, b, c, d > 0]

∴0 ≤ M ≤ 1