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प्रश्न
`1/a, 1/b` and `1/c` are in A.P. Show that : bc, ca and ab are also in A.P.
उत्तर
Since, `1/a, 1/b` and `1/c` are in A.P.
We have to show that
bc, ca and ab are also in A.P.
∵ `1/a, 1/b` and `1/c` are in A.P.
∴ `2/b = 1/a + 1/c`
`\implies 2/b = (c + a)/(ac)`
`\implies` 2ac = bc + ab or ab + bc
∴ ab, ac and bc are in A.P.
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