Question

If x/a=y/b=z/c, prove that
i. x^3/a^2+y^3/b^2+z^3/c^2=(x+y+z)^3/(a+b+c)^2​

Answer 1

Answer:

Let  x/a = y/b = z/c = k,  [By k method]

x  = ak,  y = bk  and  z = ck

L.H.S.  = a3k3/a2 + b3k3/b2 + c3k3/c2  ⇒  k3[a + b + c]

R.H.S. = [ak + bk + ck]3/[a + b + c]2  ⇒  k3[a + b + c]3/[a + b + c]2  

= k3(a + b + c)

L.H.S.  =  R.H.S.

Hence proved

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