Question

The product of three numbers in G.P is 1 & the sum of the products of their pairs is 7/2 ; find the numbers

Answer 1

let the numbers be a,ar,ar^2

now can you form equations ?

Answer 2

i know what to do first

Answer 3

yes i can form the 1st one

Answer 4

what is the 2nd one i cant understand the pair system?

Answer 5

a(ar) + a(ar^2) + (ar)(ar^2) = 7/2

-> product, in pairs <-

Answer 6

ok thanks :)

Answer 7

yw :)

Answer 8

a*ar*ar^2=1

Answer 9

yep.

Answer 10

a^3 r^3=1

Answer 11

(ar)^3=(1)^3

Answer 12

You can actually do it quicker, if you assume the 3 terms are
a/r , a and ar

but a,ar,ar^2 works fine too.

Answer 13

a/r*a*ar=1

Answer 14

a=1

Answer 15

yep, so middle term =1
use second eqn to find r.

Answer 16

(a/r)(a)+(a/r)(ar)+(a)(ar)=7/2

Answer 17

a=1,

Answer 18

make that substitution.

Answer 19

1+r+r^2=7/2 r

Answer 20

what now?

Answer 21

its a quadratic eqn in r, solve for r simply.

Answer 22

whats the quadratic equation?

Answer 23

You have never studied about quadratic equations ?

Answer 24

i meant to say that what quadratic are u getting?

Answer 25

2 + 2r + 2r^2 = 7r
=> 2r^2 - 5r +2 =0

Answer 26

2r^2-(4+1)r+2=0

Answer 27

yep, go on..

Answer 28

2r(r-2)-1(r-2)=0

Answer 29

r=2 & r=1/2

Answer 30

bingo !
congrats ! ^_^

Answer 31

so how am i supposed to get the numbers?

Answer 32

first number = a/r
second = a
third = ar

Answer 33

i have to substitute both values of r?

Answer 34

one by one,
you'll get symmetric GPs

Answer 35

2 of them

Answer 36

ok!! :)

Answer 37

thanks

Answer 38

Glad to help. :)

Answer 39

1st G.P is 1/2,1,2

Answer 40

2nd one is 2,1,1/2

Answer 41

yep.