The sum of three numbers in GP is 39/10 and their product is 1 find the number?
Answers
Answer:
Three numbers are 2/5, 1 and 5/2
Step-by-step explanation:
Let three numbers in GP are a/r, a and ar
Given that sum of three numbers in GP = 39/10
and Product of three numbers in GP = 1
Now, Product of a/r, a and ar is calculated as
a/r * a * ar = 1
a^3 = 1
a = 1
Also, sum of a/r, a and ar is calculated as
a/r + a + ar = 39/10
Substituting the value of a = 1 in above, we get
1/r + 1 + r = 39/10
10(1 + r + r^2) = 39r
10 + 10r +10r^2 = 39r
10r^2 - 29r + 10 = 0
Solving the quadratic equation using factorization, we get
10r^2 -25r -4r + 10 = 0
5r( 2r - 5) - 2(2r - 5) = 0
(5r - 2)(2r - 5) = 0
Either 5r - 2 = 0 or 2r - 5 = 0
5r = 2 or 2r = 5
r = 2/5 or r = 5/2
When r = 2/5 and a = 1, then three numbers are
5/2, 1, 2/5
When r = 5/2 and a = 1, then three numbers are
2/5, 1 ,5/2
Thus, three numbers are - 2/5, 1, 5/2