Question

hello!

if a^1/x= b^1/y=c^1/z and a,b,c are in G.P then x,y,z are in ?

Plz. explain correctly in detail step by step. ​

Answer 1

Let a,b,c are in GP

a1x=b1y=c1z=k

b2=ac

a=kx,b=ky,c=kz

k2y=kx∗Kz

2y=x+z

y+y=x+z

y−x=z−y

Therefore x,y,z are in AP

Answer 2

z , c = ky, b = kxa = k k (let) =z = c1/y = b1/x1/a

now a,b,c are in g.p. (given)

hence b/a = c/b

ky / kx = kz / ky

k(2y) = k(x +z)

hence 2y = x + z

hence x, y, z will be in A.P.

hope it helps u mark as brainliest please