Question

If  xa = cb  and xc = ca  then  prove that a2 = bc​

Answer 1

xa = cb

So ,

x = cb / a..... ( 1)

Now,

xc = ca

x = a.... ( 2)

From 1 and 2 ===

a = cb / a

a² = bc

Proved.

Answer 2

Given xa = cb ⇒ x = (cb)1/a = cb/a --------(1) and xc = ca ⇒ (cb/a)c = ca [ from (1) ] ⇒ bc / a = a ( bases are equal powers should be equated) ⇒ a2 = bc.