If a^x = b^y = c^z and a, b, c are in G.P.,th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $a, b, c$ are in $G.P.$,we have $b^2 = ac \dots (i)$.Let $a^x = b^y = c^z = k$.Then $a = k^{1/x}, b = k^{1/y}, c = k^{1/z}$.Substitutin

Vedclass · Accepted Answer

$H.P.$

Vedclass · Answer

(C) Given that $a, b, c$ are in $G.P.$,we have $b^2 = ac \dots (i)$.Let $a^x = b^y = c^z = k$.Then $a = k^{1/x}, b = k^{1/y}, c = k^{1/z}$.Substituting these values into equation $(i)$:$k^{2/y} = k^{1/x} \cdot k^{1/z} = k^{(1/x + 1/z)}$.Equating the exponents,we get $\frac{2}{y} = \frac{1}{x} + \frac{1}{z}$.This implies that $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in $A.P.$Therefore,$x, y, z$ are in $H.P.$

If $a^x = b^y = c^z$ and $a, b, c$ are in $G.P.$,then $x, y, z$ are in

Similar Questions

If $\frac{x + y}{2}, y, \frac{y + z}{2}$ are in $H.P.$,then $x, y, z$ are in

The $9^{th}$ term of the series $27 + 9 + 5\frac{2}{5} + 3\frac{6}{7} + \dots$ is:

If the harmonic mean between $a$ and $b$ is $H$,then $\frac{H + a}{H - a} + \frac{H + b}{H - b} = $

If $a, b, c$ are in $G$.$P$. $(a > 1, b > 1, c > 1)$, then for any real number $x$ $(x > 0, x \neq 1)$, the terms $\log_{a} x, \log_{b} x, \log_{c} x$ are in:

If the $5^{th}$ term of a Harmonic Progression $(H.P.)$ is $1/45$ and the $11^{th}$ term is $1/69$,then its $16^{th}$ term is...

Vedclass Test Series

Exam Paper Generator

Online Exam Module