+0  
 
0
45
2
avatar

If (x + 1/x):(x - 2/x) = 5:4, then find the value of x.

 Jun 21, 2021
 #1
avatar+120930 
+1

 (x + 1/x):(x - 2/x) = 5:4

 

x + 1/x  =    (x^2 +1)  / x               (1)

 

x - 2/x    =   (x^2 - 2)  / x               (2)

 

Diviiding (1) by (2)   we  have

 

x^2 + 1            5

______    =    ___                  cross-multiply

x^2  - 2            4

 

4x^2  +  4     =    5x^2  -  10        rearrange  as

 

 

x^2   -   14   =   0

 

x^2  =  14                take both roots

 

x = sqrt 14                   x =  -sqrt  14

 

 

cool cool cool

 Jun 21, 2021
 #2
avatar+286 
+1

Hey there, Guest!

 

So, let's go through this problem step-by-step:

 

First, let's format it like this: \(\frac{x+1/x}{x-2/x}=\frac{5}{4}\)

 

\(\frac{x^2+1}{x^2-2}=\frac{5}{4}\)

 

Step 1: Multiply both sides by \(x^2-2\).

 

\(x^2+1=\frac{5}{4}x^2+\frac{-5}{2}\)

 

\(x^2+1-\frac{5}{4}x^2=\frac{5}{4}x^2+\frac{-5}{2}-\frac{5}{4}x^2\) (Subtract \(5/4x^2\) from both sides.)

 

\(-\frac{1}{4}x^2+1=\frac{-5}{2}\)

 

\(-\frac{1}{4}x^2+1-1=-\frac{5}{2}-1\) (Subtract from both sides.)

 

\(\frac{-\frac{1}{4}x^2}{-1/4}=\frac{\frac{-7}{2}}{-1/4}\)

 

\(x^2=14\)

 

Therefore \(x=\sqrt{14}\) and \(-\sqrt{14}\).

 

Hope this helped! :)

( ゚д゚)つ Bye

 Jun 21, 2021

4 Online Users