It would help if you would proofread your work before you post it.
Clarify your post.
If 4÷3,m,1,n form a Gp what is the product of m and n
2 answers
So your terms of the GP are
4/3, m, 1, n
so a = 4/3
m = ar = (4/3)r
1 = ar^2 ----> 1 = 4/3 r^2
r^2 = 3/4
r = ± √3/2
then n = ar^3 = (4/3)(±√3/2)^3 = ± √3/2
m = ar = (4/3)(±√3/2) = ±√3
check:
4/3, √3, 1, √3/2 do form a GP, so does
4/3, -√3, 1, -√3
4/3, m, 1, n
so a = 4/3
m = ar = (4/3)r
1 = ar^2 ----> 1 = 4/3 r^2
r^2 = 3/4
r = ± √3/2
then n = ar^3 = (4/3)(±√3/2)^3 = ± √3/2
m = ar = (4/3)(±√3/2) = ±√3
check:
4/3, √3, 1, √3/2 do form a GP, so does
4/3, -√3, 1, -√3