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Pandey Ji

· started a discussion

· 1 Months ago

pr (Question: 107962.0 )

paramount you are spoiling your name by giving such solution

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

Dear Student
The only thing missing in this solution is the explanation for why the equation..
(a+b)_>2(ab)^(1/2).............................................(2)
The reason for this explanation is that we have to compute the value of (1+a)(1+b)(1+c)
and thus we can keep one of the variables as 1
And thus for that sole convenience we have taken up this equation (or per se the operating equation as equation (2)) Keep learning with us!
Thanks and regards
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