QQuestion
If a, b, c are in continued proportion, then prove that {1\over b}= {1\over b-a}+ {1\over b-c}
✓Answer
a, b, c are in continued proportion ⇒ b² = ac
LHS: {1\over b-a}+ {1\over b-c} = {(b - c) + (b - a)}\over (b-a)(b-c)
= 2b - c - a\over b² - bc - ab + ac
= 2b - c - a\over b² - bc - ab + b²
= 2b - c - a\over 2b² - bc - ab
= 2b - c - a\over b(2b - c - a)
= 1\over b : RHS
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