If {x^a} = {x^{b/2}}{z^{b/2}} = {z^c},then a, | vedclass

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

Question

(C) Let ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c} = \lambda$. From this,we have $x = \lambda^{1/a}$,$z = \lambda^{1/c}$,and $xz = \lambda^{2/b}$. Substituti

Vedclass · Accepted Answer

$H.P.$

Vedclass · Answer

(C) Let ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c} = \lambda$. From this,we have $x = \lambda^{1/a}$,$z = \lambda^{1/c}$,and $xz = \lambda^{2/b}$. Substituting the values of $x$ and $z$ into the expression for $xz$: $\lambda^{1/a} \cdot \lambda^{1/c} = \lambda^{2/b}$. Using the laws of exponents,we get $\lambda^{(1/a) + (1/c)} = \lambda^{2/b}$. Equating the exponents,we have $\frac{1}{a} + \frac{1}{c} = \frac{2}{b}$. This is the condition for $a, b, c$ to be in $H.P.$

If ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c}$,then $a, b, c$ are in

Similar Questions

$A$ boy goes from his home to school at a speed of $x \text{ km/hr}$ and returns at a speed of $y \text{ km/hr}$. What is the average speed of the boy?

If $\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in Arithmetic Progression $(AP)$,then $a^2, b^2, c^2$ are in which progression?

What is the harmonic mean of the reciprocals of the first $n$ natural numbers?

If there are $n$ harmonic means between $1$ and $\frac{1}{31}$ and the ratio of the $7^{th}$ and $(n - 1)^{th}$ harmonic means is $9:5$,then the value of $n$ is:

If ${a_1}, {a_2}, {a_3}, \dots, {a_n}$ are in $H.P.$,then the expression ${a_1}{a_2} + {a_2}{a_3} + \dots + {a_{n - 1}}{a_n}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module