If a, b, c, d are positive real numbers, such that a + b +... | MATH - nth TERM OF SPECIAL SERIES, SUM TO n TERMS AND INFINITE NUMBER OF TERMS | SolveeIt | Solveeit

Today, August 18

Question

If a, b, c, d are positive real numbers, such that

a + b + c + d = 2, then S = (a + b) (c + d) satisfy the relation

A

0 £ S £ 1

B

1 £ S £ 2

C

2 £ S £ 3

D

3 £ S £ 4

Answer

0 £ S £ 1

Explanation

Solution

If a, b, c, d ÎR⁺ and (a + b) + (c + d) = 2

Let A = a + b & B = c + d

Then $( \text { A.B } ) ^ { \frac { 1 } { 2 } }$ £

(a + b). (c + d) £ $\left( \frac { \mathrm { a } + \mathrm { b } + \mathrm { c } + \mathrm { d } } { 2 } \right) ^ { 2 }$

̃ 0 £ S £ 1