Find the Value of a²b²c² :

If
Q. 83 then the value of a²b²c² is

  1. 0
  2. -1
  3. abc
  4. 1
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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1 Answer(s)

Answer is (4): 1

Explanation:-
a + 1/b = b + 1/c = c + 1/a
(ab + 1)/b = (bc + 1)/c = (ac + 1)/c

Then, (ab + 1)/b = (bc + 1)/c
b = (ab + 1)c/(bc + 1)  & c = (bc + 1)b/(ab + 1)

And, b+ 1/c = c + 1/a
 (bc + 1)/c = (ca + 1)/a
c = (bc + 1)a/(ca + 1) & a = (ca + 1) c/(bc + 1)

a + 1/b = c + 1/a
(ab + 1)/b = (ca + 1)/a
b = (ab + 1)a/(ca + 1)  & a = (ca + 1)b/(ab + 1)

Then, a2bc2 = (ab + 1)c/(bc + 1) x (bc + 1)b/(ab + 1) x (bc + 1)a/(ca + 1) x (ca + 1) c/(bc + 1) x (ab + 1)a/(ca + 1) x  (ca + 1)b/(ab + 1)
 = 1

Then, the value of a2bc2 is 1.

Hence, the answer is (4) 1.

Monis Rasool Professor Answered on 28th October 2015.
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