Question

The four positive numbers 3, x, y, 9 are such that 3, x, y form a GP and x, y, 9 form an AP. FInd x+y. @ganeshie8

Answer 1

@perl

Answer 2

find the common ratio for the 3 term GP\[r = \frac{x}{3} = \frac{y}{x}\] cross multiply and you get

equation 1

\[\frac{x^2}{3} = y\]

now look at the 3 term AP and find the common difference

\[y - x = 9 - y~~~ or ~~~~~ 2y - x - 9 = 0\]

call this equation 2

now you need to solve simultaneous equations using the substitution method

substitute equation 1 into equation 2

\[2(\frac{x^2}{3}) - x - 9 = 0\]

multiply every term by 3

\[2x^2 - 3x - 27 = 0\]

now you have an equation that can be solved by factoring

eliminate the negative zero, and only consider the positive

when you get x, substitute into equation 1 or 2 and solve for y.

hope it helps

Answer 3

3,x,y form a GP => x^2 = 3y

x,y,9 form an AP => 2y=9+x

=> x^2 = 3(9+x)/2

=> 2x^2 -3x -27 = 0

=> 2x^2 + 6x -9x -27=0

=> (2x-9)(x+3) = 0

x=9/2 or x =-3

2y = 9 + 9/2 => 4y = 27 y = 27/4

x+y = 9/2 + 27/4 = 45/4

2y = 6 => y = 3

x+y = -3 + 3 =0

Hope its Correct...

Answer 4

0 isnt an answer option
the options are 9.5, 10, 10.5, 11.25, 13.5 @campbell_st could you check yourss cos i dont think its right

Answer 5

45/4 is 11.25 which is the answer @CrashOnce :)

Answer 6

Answer set is 11.25 or 0

Answer 7

r u sure?, i cant seem to prove that is correct...

Answer 8

3, 9/2, 27/4, 9 is the series...

=> (9/2)^2 = 3*27/4 (GP)

and

=> 2*27/4 = 27/2 and 9/2 + 9 = 27/2 (AP)

So its Correct...

Answer 9

ok... so what positive solution did you get for x...?

Answer 10

@sriramkumar the aim of open study is to assist learning and not to give answers.

Answer 11

ok thanks both of u, though @campbell_st sriamkumar provided working which was helpful

Answer 12

lol.... well I got you to the quadratic... if you are working at this level I would have expected you co factor the quadratic....

as I said before, the aim is to guide you... not to answer homework or exam questions for you.

Answer 13

sorry bout that but thanks both of u