Question

If x^a = y^b = z^c
and y^2 = xy

then show that,

1/a + 1/c = 2/b

Answer 1

you mean y^2 = xz ?

Answer 2

put x^a=y^b=z^c=t
calculate x,y,z in terms of t and then put the values of x,y,z

Answer 3

you followed or should i give you more clue.

Answer 4

cud u xplain me in detail?
@surjithayer

Answer 5

\[x ^{a}=t,x=t ^{\frac{ 1 }{ a }}\]
similarly y=?
and z=?

Answer 6

clear

Answer 7

x^a = y^b = z^c = k

x = k^(1/a)

y = k^(1/b)

z=k^(1/c)

y^2 = x*z

k^(2/b) = k^ (1/a + 1/b)

--> 2/b = 1/a + 1/b

Answer 8

soory

*1/c

Answer 9

\[x ^{a}=\left( t ^{\frac{ 1 }{a }} \right)^{a}=\left( t \right)^{\frac{ 1 }{ a }*a}=t\]