Question

for what value of x , the numbers (x+9),(x-6) and 4 are in G.P.?

Answer 1

For what value of x, the numbers (x+9),(x-6) and 4 are in g.p

Let these be in g.p so that,

(x-6)^2=4(x+9)

x2-12x+36=4x+36

x^2-16x=0

x=0 or x=16.

Therefore, when x=16, the numbers in g.p are

25,10 and 4.

where the common ratio is 2.5

25*(2.5)=10

10*(2.5)=4