Question

if G1 and G2 are inserted between two numbers a and b then show. that G1^2/G2+G2^2/G1=1​

Answer 1

Answer:

Step-by-step explanation:

if G1 and G2 are GP then

let r be the common difference then G1 = a(b/a)^1/(n+1) ,and G2 = a(b/a)^2/(n+1) where n = 2 we get

G1 =(a )^2/3(b)^1/3 and G2 = (b)^2/3 (a)1/3

now given G1/G2 +G2/G1 = 1  

putting the value of G1 and G2 we get

(a)^2/3 (b)1/3/(b)^2/3 (a)^1/3 + (b)^2/3(a)^1/3/(a)^2/3(b)1/3

(a)^1/3/(b)^1/3 + (b)^1/3/ (a)^!1/3

[(a)^2/3 + (b)^2/3 ]/(ab)^1/3