Q.

The number of positive integral ordered pairs of (a, b) such that 6, a, b are in harmonic progression is __________.

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answer is 7.

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Detailed Solution

6, a, b in H.P.⇒16,1a,1b are in A.P.⇒ 2a=16+1bor  1b=2a−16or   1b=12−a6aor   b=6a12−aa∈{3,4,6,8,9,10,11}
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The number of positive integral ordered pairs of (a, b) such that 6, a, b are in harmonic progression is __________.