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Question

Let f(x)=x+1/2, then the number of real values of x for which the three unequal terms f(x),f(2x),f(4x) are in H.P is

A
1
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B
0
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C
3
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D
2
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Solution

The correct option is A 1
Given f(x), f(2x), f(4x) are in H.P.
f(x)=x+12
f(2x)=2x+12
f(4x)=4x+12
2x+12=2(x+12)(4x+12)(x+12)+(4x+12)
4x+12=(2x+1)(8x+1)(5x+1)(2)
20x2+9x+1=16x2+10x+1
4x2x=0
x=0 or x=14.
For x=0, we get each of f(x),f(2x), and f(4x) are all equal.
Hence, x=14 is the only real value of x that meets the criteria.

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