Quantities x, 8, y (x=/y) are in g.p. and x, y, -8 in a.p. Find the value of x and y.

Answer 1

first condition:
8/x = y/8
xy = 64

2nd condition:
y-x = -8-y
2y + 8 = x

in xy=64
(2y+8)(y) = 64
2y^2 + 8y - 64=0
y^2 + 4y - 32=0
(y+8)(y-4) = 0
y = -8 or y = 4

since xy= 64
if y = 4, x = 16
if y = -8 , x = -4

Answer 2

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