If-a-b-c-d-are-in-GP-and-a-x-b-y-c-z-d-u-then-x-y-z-u-are-in-

Question Number 18448 by ankit kumar sharma last updated on 21/Jul/17

If a, b, c, d are in GP and a^{x} = b^{y} = c^{z} = d^{u},

then x, y, z, u are in

Answered by Tinkutara last updated on 21/Jul/17

b^{2} = a c, c^{2} = b d

a = k^{\frac{1}{x}}, b = k^{\frac{1}{y}}, c = k^{\frac{1}{z}}, d = k^{\frac{1}{u}}

k^{\frac{2}{y}} = k^{\frac{1}{x} + \frac{1}{z}}, k^{\frac{2}{z}} = k^{\frac{1}{y} + \frac{1}{u}}

∴ x, y, z and u are in H . P .