Question

Solve the inequality that x minus one upon x minus 2 is less than equal to zero

Answer 1

Given :  x  - 1/x   - 2  ≤ 0    

To find : Solve for x

Solution:

x  - 1/x   - 2  ≤ 0    

at x = 0 not defined as  1/x

case 1  :

x >  0

Multiply both sides by x

=> x²  - 1 - 2x   ≤ 0

=> (x - 1)² - 1 - 1 ≤ 0

=> (x - 1)² ≤  2

=>    -√2 ≤   x -  1 ≤ √2

=>    -√2 + 1 ≤   x   ≤ √2 + 1

x > 0

=>  x  ∈ ( 0 , √2 + 1]

case 1  :

x <  0

Multiply both sides by x

=> x²  - 1 - 2x   ≥ 0  

=> (x - 1)² - 1 - 1   ≥ 0

=> (x - 1)²   ≥  2

as x < 0

=> x - 1 ≤  - √2

=> x ≤  1 - √2

=>  x  ∈ ( -∞ ,  1 - √2 ]

x  ∈ ( -∞ ,  1 - √2 ] ∪  x  ∈ ( 0 , √2 + 1]

Learn more:

Solve the inequality. $log_3 dfrac{|x^2-4x|+3}{x^2+|x-5|} geq 0$

https://brainly.in/question/17291985

Solve the inequality -3 ≤ 4 -7x/2 ≤ 18 - Brainly.in

https://brainly.in/question/17175140

Answer 2

Step-by-step explanation:

Solve the inequality that x minus one upon x minus 2 is less than equal to zero