Question

if A^x=B^y=c^z and a^2=bc then z equal to​

Answer 1

Let, a^x=b^y=c^z=k then expressing a, b, c in terms of k we have, k^1/x=a, k^1/y=b, k^1/z=c. Putting in second equation we get, k^2/x=k^1/y.k^1/z

k^2/x=k^1y+1/z

2/x=1/y+1/z

On solving further we have, z=xy/2-x(writing z in terms of x, y, constants).

Answer 2

Answer:

Let a

x

=b

y

=c

z

=k .....( Given )

∵a

x

=k

⇒a=k

x

1

∵b

y

=k

⇒b=k

y

1

.....∵c

z

=k

⇒c=k

z

1

Given, b

2

=ac

Substituting values of a,b,c in above equation

(k

y

1

)

2

=k

x

1

×k

z

1

⇒k

y

2

=k

x

1

+

z

1

⇒

y

2

=

x

1

+

z

1

⇒

y

2

=

xz

x+z

⇒y=

x+z

2xz