Find the mean proportion between a-b/a+b and a²b²/a²-b²
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Solution :-
we know that,
- Mean proportion of x and y = √(x * y)
we have,
- x = (a - b) / (a + b)
- y = (a²b²) / (a² - b²)
so,
→ Mean proportion = √[{(a - b) / (a + b)} * {(a²b²) / (a² - b²)}]
→ Mean proportion = √[{(a - b)(a²b²)} / {(a + b)(a² - b²)}]
putting :-
- a² - b² = (a + b)(a - b)
→ Mean proportion = √[(a²b²) / (a + b)²]
→ Mean proportion = ab / (a + b) (Ans.)
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