Two geometric means a, b are inserted between x and y such that a3 + b3 = n (ab) A,
where A is the arithmetic mean of x and y. What is value of n?
Two geometric means a, b are inserted between x and y such that a3 + b3 = n (ab) A, where A is the arithmetic mean of x and y. What is value of n?
Option 1 -
1
Option 2 -
2
Option 3 -
3
Option 4 -
4
Asked by Shiksha User
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1 Answer
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Correct Option - 2
Detailed Solution:x, a, b, y are in GP
a = xr
b = xr2
y = xr3
r =
rewrite,
a = x2/3.y1/3
b = x1/3.y2/3
a × b = x × y
a3 + b3 = x2y + y2 x
= xy (x+y)
= xy (2A) ……………
Hence, n = 2
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