Question

Given x y z are in gp and x^p=y^q=z^r then 1/p 1/q 1/r are in

Answer 1

Answer:

there in ap

Step-by-step explanation:

if x,y and z are in g.p then y^2=xz, y=√(xz)

given x^p=y^q=z^r

consider x^p=y^q

x^p=((xz)^(1/2))^q

x^p=x^(q/2) . z^(q/2)

in left handed side the powers of x is equal to the right handed side

therefore, p=(q/2)

now, consider y^q=z^r

((xz)^(1/2))^q=z^r

x^(q/2). z^(q/2)=z^r

in left handed side the powers of x is equal to the right handed side

therefore, r=(q/2)

p=r=(q/2)

consider p+r=(q/2)+(q/2)

p+r= q

consider (1/p)+(1/r)=(p+r)/pq

=q/(q/2)(q/2)

=q/((q^2)/2)

=2/q

therefore (1/p)+(1/r)=(2/q)

this the condition of ap

Answer 2

Answer:

(a) ------> A.P

I HOPE UR DOUBT GOT COMPLETELY CLEARED...

I HOPE UR DOUBT GOT COMPLETELY CLEARED...PLEASE MARK ME AS BRAINLIEST