Question

if x=a(b-C) y=b(c-a) z= c(a-b) then find (x^3/a^3)+(y^3/b^3)+(z^3/c^3)=

Answer 1

You can see x/a + y/b + z/c = (b-c) + (c-a) + (a-b) = 0. You might be knowing a common algebraic property p+q+r=0 ⇔ p³+q³+r³=3pqr. From this you have (x/a)³+(y/b)³+(z/c)³=3(x/a)(y/b)(z/c). Hence, answer is 3(a-b)(b-c)(c-a)