KnowledgeBoat Logo

Mathematics

Find the value of x so that 2x - 1, 5x - 6, 6x + 2 and 15x - 9 are in continued proportion.

Ratio Proportion

3 Likes

Answer

Given,

2x - 1, 5x - 6, 6x + 2 and 15x - 9 are in continued proportion.

∴2x−15x−6=6x+215x−9⇒(2x−1)(15x−9)=(5x−6)(6x+2)⇒30x2−18x−15x+9=30x2+10x−36x−12⇒30x2−33x+9=30x2−26x−12⇒30x2−30x2−26x+33x=9+12⇒7x=21⇒x=217=3.\therefore \dfrac{2x - 1}{5x - 6} = \dfrac{6x + 2}{15x - 9} \\[1em] \Rightarrow (2x - 1)(15x - 9) = (5x - 6)(6x + 2) \\[1em] \Rightarrow 30x^2 - 18x - 15x + 9 = 30x^2 + 10x - 36x - 12 \\[1em] \Rightarrow 30x^2 - 33x + 9 = 30x^2 - 26x - 12 \\[1em] \Rightarrow 30x^2 - 30x^2 - 26x + 33x = 9 + 12 \\[1em] \Rightarrow 7x = 21 \\[1em] \Rightarrow x = \dfrac{21}{7} = 3.

Hence, x = 3.

Answered By

1 Like

Related Questions