0
Three numbers in GP sum up to 21. Their product is 216. Find the numbers.?
Sonujan12
Let a be the first of the three number and r the common ratio. Then
a*ar*ar2 = a3r3 = 216 = 63 so that ar = 6
Also, a + ar + ar2 = 21
Substitute ar = 6 to give 6/r + 6 + 6r = 21 or 6 + 6r + 6r2 = 21r
So that 6r2 - 15r + 6 = 0 or 2r2 - 5r + 2 = 0
2r2 - 4r - r + 2 = 0 or 2r*(r-2) - 1(r-2) = 0 or (2r-1)*(r-2) = 0 so r = 0.5 or r = 2
r = 0.5 gives the three numbers as being 12, 6, 3
and r = 2 gives 3, 6, 12.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
How do you find the sum of 216 with three numbers?
71 + 72 + 73 = 216
The sum of three consecutive numbers is 216 what are the three numbers?
71,72,73 :)
The sum of the three consecutive numbers is 216?
The numbers are 71, 72 and 73.
The sum of 4 consecutive three digit numbers is 866 what are the 4 numbers?
215 + 216 + 217 + 218 = 866
What The product of 6 and m is 216?
It is equivalent to the equation: 6m = 216
Three numbers in GP sum up to 21. Their product is 216. Find the numbers?
3 + 6 + 12 = 21 3 x 6 x 12 = 216
How do you find the sum of 216 with three numbers?
71 + 72 + 73 = 216
What is 216 as the product of prime numbers?
216 = 2x2x2x3x3x3
What is the 3 consesecutive numbers of 216?
the sum of three consecutive numbers is 216. What are the three numbers?
The sum of three consecutive numbers is 216 what are the three numbers?
71,72,73 :)
Express 216 as the product of prime numbers in index form?
23 x 33 = 216
The sum of the 3 numbers is 21 the product is 336. What are the numbers?
6 + 7 + 8 = 216 x 7 x 8 = 336Therefore, the three numbers are 6, 7 and 8.
What is 216 expressed in prime numbers?
As a product of its prime factors expressed in exponents it is: 23*33 = 216
The sum of three conecutive numbers is 216 what are those three numbers?
divide 216 by 3 (72) subtract 1 and add 1 71, 72 and 73
The sum of the three consecutive numbers is 216?
The numbers are 71, 72 and 73.
The sum of three consecutive numbers is 216 what are the four numberswith238?
For 216 the numbers are 70, 72 and 74. For 238 the numbers are 58, 59, 60 and 61.
What are three consecutive numbers that add up to 216?
x+x+1+x+2=216 3x+3=216 3x=213 71,72,73
