KnowledgeBoat Logo
|

Mathematics

Find the mean proportion to (x - y) and (x3 - x2y)

Ratio Proportion

18 Likes

Answer

Let mean proportion to (x - y) and (x3 - x2y) be a.

∴x−ya=ax3−x2y⇒a2=(x−y)(x3−x2y)⇒a2=(x−y).x2.(x−y)⇒a2=x2.(x−y)2⇒a=x(x−y).\therefore \dfrac{x - y}{a} = \dfrac{a}{x^3 - x^2y} \\[1em] \Rightarrow a^2 = (x - y)(x^3 - x^2y) \\[1em] \Rightarrow a^2 = (x - y).x^2.(x - y) \\[1em] \Rightarrow a^2 = x^2.(x - y)^2 \\[1em] \Rightarrow a = x(x - y).

Hence, mean proportion to (x - y) and (x3 - x2y) = x(x - y).

Answered By

9 Likes

Related Questions