Question

Solve each of the following equations by factorization: 

`x+1/x=2.5` 

Answer 1

`x+1/x=2.5`  

⇒ `(x^2+1)/x=5/2` 

⟹ `2x^2 + 2 = 5x`
⟹ `2x^2 – 5x + 2 = 0`
⟹ `2x^2 – 4x – x + 2 = 0`
⟹ 2x (x – 2) – 1 (x – 2) = 0
⟹ (x – 2) (2x – 1) = 0
Since x – 2 = 0 Or 2x – 1 = 0 

Then `x=2 or x=1/2`