If b + c = ax, c + a = by, a + b = cz, then the value of 1/9[1/(x + 1) + 1/(y + 1) + 1/(1/z + 1)] is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 1/9
⇒ b + c = ax ⇔ x = (b + c)/a
⇒ a + c = by ⇔ y = (a + c)/b
⇒ b + a = cz ⇔ z = (b + a)/c
⇒ 1/9[1/((b + c)/a + 1) + 1/((a + c)/b + 1) + 1/(1/(b + a)/c + 1)]
⇒ 1/9[(a/a + b + c) + (b/a + b + c) + (c/a + b + c)]
⇒ 1/9[(a + b + c)/(a + b + c)]
⇒ 1/9