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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