Find the mean proportion of $\frac{a^3+b^3}{a-b}$ and $\frac{a^2-b^2}{a^2-a b+b^2}$.
Answer & explanation
Correct answer: option 2
Using direct formula,
Mean Proportion = \(\sqrt {a\; \times\; b }\)
= \(\sqrt { (\frac{a^3+b^3}{a-b})\; \times\; (\frac{a^2-b^2}{a^2-a b+b^2})}\)
= \(\sqrt {\frac{ (a + b)(a² - ab + b² )}{(a - b)}\; \times\; \frac{(a+b)(a-b)}{a^2-a b+b^2} }\)
(using the formula a³ + b³ = (a + b)(a² - ab + b² ) and a² - b² = (a + b)(a - b))
= ( a + b)