Grade 11Algebra
if a b c are in gp and a^1/x=b^1/y=c^1/z prove that x y z are in ap
if a b c are in gp and a^1/x=b^1/y=c^1/z prove that x y z are in ap
3 Answers
Arun
z , c = ky, b = kxa = k k (let) =z = c1/y = b1/x1/a
now a,b,c are in g.p. (given)
hence b/a = c/b
ky / kx = kz / ky
k(2y) = k(x +z)
hence 2y = x + z
hence x, y, z will be in A.P.
Mohd Mujtaba
Let a^1/x=b^1/y=c^1/z=m .soa=m^x,b=m^y, c=m^z. Now a b c are in gp so b^2=ac. This imply m^2y=m^z.m^x so comparing we get 2y=x+z. Hence a b c are in ap thank☺☺☺☺
Kushagra Madhukar
Dear student,
Please find the attached solution to your question
Let,
a1/x = b1/y = c1/z = k
Hence,
a = kx, b = ky, c = kz
Since a, b, c are in GP
b2 = ac
k2y = k(x+z)
or, 2y = x + z
Hence, x, y, z are in A.P.
Hope it helps.
Thanks and regards,
Kushagra
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago