Question

if x/a=y/b=z/c, then value of x3/a3-y3/b3+z3/c3 is​

Answer 1

I think your question is incomplete. question should be ---> If x/a=y/b=z/c prove that x3/a3 - y3/b3 + z3/c3 = xyz/abc.

solution : x/a = y/b = z/c = k (let)

then x = ak .....(1)

y = bk ......(2)

and z = ck.....(3)

LHS = x³/a³ - y³/b³ + z³/c³

= (x/a)³ - (y/b)³ + (z/c)³

from equations (1), (2) and (3),

= (ak/a)³ - (bk/b)³ + (ck/c)³

= k³ - k³ + k³

= k³

RHS = xyz/abc

= (x/a).(y/b).(z/c)

from equations (1), (2) and (3),

= (ak/a).(bk/b).(ck/c)

= k.k.k

= k³

here it is clear that LHS = RHS

hence, x³/a³ -y³/b³ + z³/c³ = xyz/abc proved