# Find the Value of a²b²c² :

**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, a^{2}bc^{2} = (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 a^{2}bc^{2} is 1.

Hence, the answer is (4) 1.