KnowledgeBoat Logo

Mathematics

If x + 5 is the mean proportion of x + 2 and x + 9, find the value of x.

Ratio Proportion

1 Like

Answer

Given,

x + 5 is the mean proportion of x + 2 and x + 9.

∴x+2x+5=x+5x+9⇒(x+2)(x+9)=(x+5)2⇒x2+9x+2x+18=x2+25+10x⇒x2+11x+18=x2+25+10x⇒x2−x2+11x−10x=25−18⇒x=7.\therefore \dfrac{x + 2}{x + 5} = \dfrac{x + 5}{x + 9} \\[1em] \Rightarrow (x + 2)(x + 9) = (x + 5)^2 \\[1em] \Rightarrow x^2 + 9x + 2x + 18 = x^2 + 25 + 10x \\[1em] \Rightarrow x^2 + 11x + 18 = x^2 + 25 + 10x \\[1em] \Rightarrow x^2 - x^2 + 11x - 10x = 25 - 18 \\[1em] \Rightarrow x = 7.

Hence, x = 7.

Answered By

1 Like

Related Questions