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# ratio question

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

Jun 21, 2021

#1
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(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   Jun 21, 2021
#2
+3

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