Question

Three rational numbers x, y, z are in G.P. Sum of the
numbers is 65 and the product of the first and third
numbers is 225. Find the common ratio of the G.P.
​

Answer 1

x,y,z,....

common ratio, r=y/x=z/y

given, x+y+z=65......1

xz=225. .......2

y/x=z/y

y²=xz

y²=225

y=15

according eqn1

x+y+z=65

x+z=65-15

x+z=50

z=50-x,

put value of z in eqn 2,

x(50-x)=225

50x-x²=225

x²-50x+225=0

x²-45x-5x+225=0

(x-45)(x-5)=0

x=45,5

z=5,45

y=15,15

x=5, y=15,z=45

x=45,y=15,z=5