Question

x - 3 = $\frac{1}{x-5}$

Answer 1

$x-3= \frac{1}{x-5} <=> (x-3)(x-5) = 1 <=> x^2-5x-3x+15-1=0 \\ x^2 - 8x + 14 = 0<=> \\ a=1 \\ b=-8 \\ c=14$

Aplica bashkara:

Δ = b² - 4ac = (-8)² - 4x1x14 = 64 - 56 = 8 

x = (-b + √Δ)/2a v x = (-b - √Δ)/2a <=>
<=> x = (-(-8) + √8)/2   v  x= (-(-8) - √8)/2 <=>
<=> x = (8 + 2√2)/2 v  X = (8 - 2√2)/2 
<=> x = 4 + √2 V x = 4 - √2 



8|2
4|2
2|2
1

8=2² x 2