Question

Find 5 numbers in Gp such that
their sum is 31/4 and product is 1​

Answer 1

Answer:

We can start with assuming the terms as ar2,ar,a,ar,ar2. ..........…….....(1)

We find only real solutions.

Since product is  a5=1. we get a=1. .........……………………………...(2)

Since the sum is  314  we get  1r2+1r+1+r+r2=314  

This equation can be rewritten as  (r+1r)2−2+1+(r+1r)−314=0  

ie (r+1r)2+(r+1r)−354=0  

ie  y2+y−354=0 where  y=r+1r    

Solving this quadratic equation we get  y=52,−72.  

Solving the corresponding equations in the variable  r we get

r=2,12,−7+33√4,−7−33√4. .........……......…………………....(3)

From (1) ,(2) and (3) we can find all possible solutions.

Step-by-step explanation: