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Question

Let f(x) = 2x + 1. Then the number of real values of x for which the three numbers f(x), f(2x), f(4x) are in G.P. is


Solution

f(x), f(2x), f(4x) are in G.P. We will replace x by 2x and 4x while finding f(2x) and f(4x)

[f(2x)]2 = f(x)f(4x)

(2(2x)+1)2 = (2x + 1)(2 ×(4x) + 1) 

(4x+1)2 = (2x+1)(8x+1)

16 x2 + 8x + 1 = 16 x2 + 10x + 1

2x = 0
x = 0

Only one value

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