Question

and
The sum of three numbers in G.P. is 1
their product is 1. Find the numbers.​

Answer 1

Answer:

let the numbers a/r,a,ar

a/r*a*ar=1

a³=1

a=1

a/r+a+ar=1

1/r+1+1*r=1

r²=1

r=1

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Answer 2

Answer:

1/i ,  1 ,  i

Step-by-step explanation:

Let the numbers of GP be as below:

First term = a/r,

2nd term = a

3rd term = ar.

Given,

Product of three numbers = 1

Sum of three numbers = 1

Since product of three numbers = 1

=> a/r * a * ar = 1

=> a³ = 1

=> a = 1.

Sum of three numbers = 1

=> a/r + a + ar = 1

=> 1/r + 1 + r = 1

=> r² + r + 1 = r

=> r² + 1 = 0

=> r² =  - 1

=> r = √-1 = i.

Thus the three numbers are 1/i, 1, i.