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Let the harmonic mean of two positive re...

Let the harmonic mean of two positive real numbers a and b be 4, If q is a positive real number such that a, 5, q, b is an arithmetic progression, then the value(s) of |q -a| is (are)

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`4=(2ab)/(a+b)`
`(ab)/(a+b)=2-(1)`
a,5,q,b->AP common diff. d
`a=5-d-(2)`
`q=a+2d`
`b=a+3d`
`b=5+2d-(3)`
`((5-d)(5+2d))/(10+d)=2`
...
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