Page 25 - Elementary Algebra Exercise Book I

ELEMENTARY ALGEBRA EXERCISE BOOK I reAl numBers

1 1 1
1.67 x,y,z are real numbers, 3x, 4y, 5z follow a geometric sequence, and , ,
x y z
x z
follow an arithmetic sequence, find the value of + .
z x
Solution:

(4y) 2 = 15xz (i)
2 1 1
= + (ii)
y x z

x,y,z
2xz
(ii) ⇒ = x+z , substitute it into (i):
2 2
2xz (x + z) 64 x z 64 x z 34
16 = 15xz ⇒ = ⇒ + 2+ = ⇒ + =
x + z xz 15 z x 15 z x 15.

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