Question

sum of two numbers is 6 times their geometric means , show that the numbers are in this ratio

Answer 1

ratio is \[3+2\sqrt{2}:3- 2\sqrt{2}\]

Answer 2

let gm be a and the numbers be x and y

a^2 = xy

x + y = 6xy

Answer 3

sorry

x + y = 6(xy)^1/2

Answer 4

dont you have any other information

Answer 5

nope

Answer 6

x + y - 6(xy)^1/2 = 0

(x^1/2 - y^1/2)^2 = 4(xy)^1/2

Answer 7

rhs = x -x + y - y + 2(xy)^1/2 + 2 (xy)^1/2

Answer 8

rhs = -(x^1/2 - y^1/2)^2 + (x^1/2 + y^1/2)^2

Answer 9

2 ( x^1/2 - y^1/2)^2 = (x^1/2 + y^1/2)^2

Answer 10

a + b = 6*\[\sqrt{ab}\]
squaring...
a^2 + b^2 +2ab=36ab
..divide by b^2
(a/b)^2 -34(a/b) +1=0..

solving quadratic eqn
a/b=33.970

reqd...ratio

Answer 11

x^1/2 + y^1/2
2^1/2 = --------------------------
x^1/2 - y^1/2

Answer 12

2^1/2 + 1 2 x^1/2
--------- = ------------
2^1/2 - 1 2 y^1/2

square both sides

2.2^1/2 + 3 x
------------- = -----
3 -2.2^1/2 y

Answer 13

there goes your answer : )

Answer 14

got it ?

Answer 15

ok