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

0 \leq M \leq 1

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1 \leq M \leq 2

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2 \leq M \leq 3

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3 \leq M \leq 4

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Solution

The correct option is A $0 \leq M \leq 1$
Given:
$a, b, c, d$ are positive real number

$\Rightarrow$ $a + b + c + d = 2 a n d M = (a + b)) c + d)$

Solution:
Since we know for two positive number Arthematic mean $\geq$ Geometric mean

Let us consider $(a + b) a n d (c + d)$ as two numbers

Hence $A . M \geq G . M$

$\Rightarrow$ $\frac{(a + b) + (c + d)}{2} \geq \sqrt{(a + b) (c + d)}$

$\Rightarrow$ $\frac{2}{2} \geq \sqrt{M}$

$\Rightarrow 0 \leq M \leq 1$

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

The correct option is A 0≤M≤1Given:a,b,c,d are positive real number⇒a+b+c+d=2 and M=(a+b))c+d)Solution:Since we know for two positive number Arthematic mean≥ Geometric meanLet us consider(a+b)and(c+d) as two numbersHence A.M≥G.M⇒(a+b)+(c+d)2≥√(a+b)(c+d)⇒22≥√M⇒0≤M≤1

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