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Real Numbers

If a , b , ...

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

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Solution

$\begin{matrix} W e k n o w t h a t a + b + c + d = 2 sin c e M = (a + b) (c + d) m u l t i p l y w i t h 1.9 \times 0.1 W h i c h i s t h e h i g h e s t w a y i n w h i c h w e c a n d i v i d e 2 T h e n w e g e t 0.19 w h i c h i s l e s s t h a n 1 s o, n o w w e k n o w t h a t M \geq= 0 W e g e t t h e h i g e s t w h e n 1 \times 1 i s t a k e n w e g e t 1 a n d n o w H e n c e, t h a t i s t h e r e q u i r e d a n s w e r . \end{matrix}$

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