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Venus

· started a discussion

· 1 Months ago

Why we are not taking a=-2, b=-2 & c=2 ? (Question: 107962.0 )

If we take a=-2, b=-2 & c=2 , satisfying abc=8 then minimum value could be 3 .i.e (1-2)(1-2)(1+2) ==> 3
which is less than 16root2.

Question:

If a + b + c = 1, then Find max value of  (1+a) (1+b) (1+c)?

Options:
A) 1.47
B) 2.87
C) 55 / 27
D) 2.37
Solution:
Ans: (d) Given,  a + b + c = 1

            

            a = \(\frac{1}{3}\), b = \(\frac{1}{3}\), c = \(\frac{1}{3}\)(for max value)

           a + b + c =1

           \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = 1

           \(\frac{3}{3}\) = 1

            1 = 1

            put the value of a, b, c 

            (1 + a) (1 + b) (1 + c)

            (1 + \(\frac{1}{3}\) ) (1 + \(\frac{1}{3}\) ) (1 + \(\frac{1}{3}\) ) 

             \(\frac{4}{3}\) × \(\frac{4}{3}\) × \(\frac{4}{3}\)

             \(\frac{64}{27}\) = 2.37 

Knowledge Expert

· commented

· 1 Months ago

(√a-1)^2>=0
=>(a+1)>= 2√a


Therefore,

(a+1)(b+1)(c+1)≥(2√a)(2√b)(2√c)
=>(a+1)(b+1)(c+1)≥(8√abc)
=>(a+1)(b+1)(c+1)≥8√8
=>(a+1)(b+1)(c+1)≥16√2 answer

Anirudh Nigam

· commented

· 1 Months ago

perhaps because it is not mentioned in options
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