Question

if (y/z)^a × (z/x)^b × (x/y)^c=1, prove that (y/z)^1/(b-c) = (z-x)^1/(c-a) = (x/y)^1/(a-b)​

Answer 1

Answer:

Step-by-step explanation:

As

(

y

z

)

a

⋅

(

z

x

)

b

⋅

(

x

y

)

c

=

1

x

c

−

b

y

a

−

c

z

b

−

a

=

1

.........(A)

Let

(

y

z

)

1

b

−

c

=

k

then

y

=

k

b

−

c

z

and putting this in (A), we get

x

c

−

b

k

(

b

−

c

)

(

a

−

c

)

z

a

−

c

z

b

−

a

=

1

or

x

c

−

b

k

(

b

−

c

)

(

a

−

c

)

z

b

−

c

=

1

or

(

z

x

)

b

−

c

=

k

(

b

−

c

)

(

c

−

a

)

(-note change from

a

−

c

to

c

−

a

)

or

z

x

=

k

c

−

a

or

(

z

x

)

1

c

−

a

=

k

Similarly

(

x

y

)

1

a

−

b

=

k

Hence

(

y

z

)

1

b

−

c

=

(

z

x

)

1

c

−

a

=

(

x

y

)

1

a

−

b