a3+b3=9 and a+b=3 then the value of 1/a+1/b is

A      1/2

b     3/2

c     5/2

d    -1

mohit007 Default Asked on 18th March 2016 in Maths.
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1 Answer(s)

Answer: (b) 3/2

Solution:-
a^3 + b^3 = 9  …………………….. (1)
And a +b = 3         ………………… (2)

Now,
a + b = 3
Cube on both side,
(a + b)^3 = 3^3
a^3 + b^3 + 3 a b (a + b) = 3 x 3 x 3
From equation (1) & (2)
9 + 3 a b x 3 = 27
9 ab = 27 – 9
9 ab = 18
ab = 18/9
ab = 2 …………………….. (3)

Then,
1/a + 1/b = (a + b)/ab
From equation (2) & (3)
(a + b)/ab = 3/2

Then, the value of 1/a + 1/b is 3/2.

Hence, the correct answer is option  (b) 3/2.

Anurag Mishra Professor Answered on 18th March 2016.
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