Write the solution set of the inequation \(x\) + \(\frac{1}{x}\) ≥

1.	Write the solution set of the inequation \(x\) + \(\frac{1}{x}\) ≥ 2.x + 1/x ≥ 2.
Answer» x + 1/x ≥ 2 ⇒ \(x\) + \(\frac{1}{x}\) - 2 ≥ 0 ⇒ \(\frac{x^2-2x+1}{x}\) ≥ 0 Case I : x² – 2x + 1 ≥ 0 and x > 0 (x – 1)² ≥ 0 and x > 0 So, by taking intersection x > 0 Case II : x² – 2x + 1 ≤ 0 and x < 0 (x – 1)² ≤ 0 and x < 0 Square term is always positive so case II is irrelevant. Then, The final answer of question is x ∈ (0, ∞).

Write the solution set of the inequation \(x\) + \(\frac{1}{x}\) ≥ 2.x + 1/x ≥ 2.

Answer»

x + 1/x ≥ 2

⇒ \(x\) + \(\frac{1}{x}\) - 2 ≥ 0

⇒ \(\frac{x^2-2x+1}{x}\) ≥ 0

Case I : x² – 2x + 1 ≥ 0 and x > 0

(x – 1)² ≥ 0 and x > 0

So, by taking intersection x > 0

Case II : x² – 2x + 1 ≤ 0 and x < 0

(x – 1)² ≤ 0 and x < 0

Square term is always positive so case II is irrelevant.

Then,

The final answer of question is x ∈ (0, ∞).