If x = a (b - c)
y = b (c - a)
z = c (a - b)
then find the value of \(\left[\frac{(x+y)\;(y+z)\;(z+x)}{5xyz}\right]\)
Answer & explanation
Correct answer: option 1
x = ab - ac
y = bc - ba
z = ca - cb
⇒ x + y + z = ab - ac + bc - ba + ca - cb = 0
So,
⇒ x + y = -z
⇒ y + z = -x
⇒ z + x = -y
Put the values:
⇒ \(\left[\frac{(x+y)\;(y+z)\;(z+x)}{5xyz}\right]\) = \(\frac{(-x)×(-y)×(-z)}{5xyz}\)
= -\(\frac{1}{5}\)