Question

If a, b, c be in A.P. & x, y, z in G.P. Prove that
x^b. y^c .z^a=x^c. y^a. z^b​

Answer 1

Answer:

Given a,b,c are in A.P

⟹2b=a+c

And also x,y,z are in G.P

⟹y=

xz

​

LHS=x

b−c

.y

c−a

.z

a−b

=x

b−c

.z

a−b

.(

xz

​

)

c−a

=x

b−c

.z

a−b

.x

2

c−a

​

.z

2

c−a

​

=x

2

2b−(a+c)

​

z

2

2b−(a+c)

​

=x

0

.z

0

=1

Step-by-step explanation: