A) 2
B) 4
C) 8
D) 16
Correct Answer: C
Solution :
\[{{\log }_{2}}(a+b)+{{\log }_{2}}(c+d)\ge 4\]\[\Rightarrow \]\[{{\log }_{2}}\{(a+b)(c+d)\}\ge 4\] |
\[\Rightarrow \]\[(a+b)(c+d)\ge {{2}^{4}}\] |
But \[A.M\ge G.M.\] |
\[\therefore \]\[\frac{(a+b)+(c+d)}{2}\ge \sqrt{(a+b)(c+d)}={{2}^{2}}\] |
\[\therefore \]\[a+b+c+d\ge 8.\] |
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