Question

28. If x = a(b-c), y = b(c - a), z = c(a - b), find the value of
Or
2​

Answer 1

Answer:

x + y  + z = 0

(x/a)³ + (y/b)³ + (z/c)³ = 3xyz/abc

Step-by-step explanation:

x = a(b-c)

=>x = ab - ac

y = b(c - a)

=>y = bc - ba

z = c(a - b)

=> z = ca - cb

x + y  + z = ab - ac + bc - ba + ca - cb

=> x + y  + z = (ab + bc + ca) - (ac + ba + cb)

=> x + y  + z = (ab + bc + ac) - (ac + ab + bc)

=> x + y  + z = 0

x/a = b - c

y/b = c-a

z/c = a - b

(x/a) + (y/b) + (z/c) = 0

we know that when p + q + r = 0

=> p³ + q³ + r³ = 3 pqr

=> (x/a)³ + (y/b)³ + (z/c)³ = 3(x/a)(y/b)(z/c)

=>  (x/a)³ + (y/b)³ + (z/c)³ = 3xyz/abc