Question

(2x-5):(3x+1) is the duplicate ratio and of 2:3, find the value of x.

Answer 1

Answer :

We know : Duplicate Ratio, of two numbers, means the ratio of their squares. So

$$\begin{gathered} \frac{\left(2x-5\right)}{\left(3x+1\right)}=\frac{2^2}{3^2} \\ \Rightarrow \frac{2x-5}{3x+1}=\frac{4}{9} \\ \Rightarrow 18x-45=12x+4 \\ \Rightarrow 6x=49 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{49}}{\mathbf{6}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)} \end{gathered}$$