the sum of three numbers in GP is 35 and their product is 1000. Find the numbers
Answers
Answer:
Three numbers are 5,10,20
Step-by-step explanation:
In this question
We have been given that
Sum of three numbers of G.P are 35 and their product is 1000.
We need to find the Three numbers which are in G.P
Let three numbers of G.P are \frac{a}{r},a,arra,a,ar
Product of 3 numbers
a.\frac{a}{r}.ar\ =\ 1000a.ra.ar = 1000
a^{3}\ =\ 1000a3 = 1000
a\ =\ 10a = 10
a = 10
Sum of three numbers is 35
Therefore, \frac{a}{r}\ +\ a\ +\ ar\ =\ 35ra + a + ar = 35
Putting the value of a as 10 we get,
\frac{10}{r}\ +\ 10\ +\ 10r\ =\ 35r10 + 10 + 10r = 35
Taking L.C.M we get,
10r^{2}\ +\ 10r\ +\ 10\ =\ 35r10r2 + 10r + 10 = 35r
10r^{2}\ -\ 25r\ +\ 10\ =\ 010r2 − 25r + 10 = 0
2r^{2}\ -\ 5r\ +\ 2\ =\ 02r2 − 5r + 2 = 0
On solving we get r = 2,\frac{1}{2}2,21
Putting the value of a and r simultaneously we get,
5,10,20 as three numbers
