`x^2-2x+3 ≤ 2x`

`⇔ x^2-2x-2x+3 ≤0`

`⇔ x^2-4x+3 ≤0`

`⇔ (x^2-9)-(4x-12) ≤0`

`⇔ (x-3)(x+3)-4(x-3) ≤0`

`⇔ (x-3)(x+3-4) ≤0`

`⇔ (x-3)(x-1) ≤0`

* TH1:

`x-3 ≥0 ⇔ x≥3`

`x-1 ≤0 ⇔ x≤1`

`=> 1≥x≥3` (vô lý)

* TH 2:

`x-3 ≤0 ⇔ x≤3`

`x-1 ≥0 ⇔ x≥1`

`=> 1≤x≤3`

Vậy `S={x|1≤x≤3}`

 

 ` x^2 - 2x + 3 ≤ 2x `

`<=> x^2 - 2x + 3 - 2x ≤ 0 `

`<=> x^2 - 4x + 3 ≤ 0 `

`<=> x^2 - 3x - x + 3 ≤ 0 `

`<=> x ( x - 3 ) - ( x - 3 ) ≤ 0 `

`<=> ( x - 3 ) ( x - 1 ) ≤ 0 `

`@)` Trường hợp `1 : `

`<=>`\(\left[ \begin{array}{l}\begin{cases} x - 3≥ 0\\ x - 1 ≤ 0 \end{cases} \\\begin{cases} x ≥ 3 \\x ≤ 1 \end{cases} \end{array} \right.\) ( vô lí )

`@)` Trường hợp `2 :` 

`<=>`\(\left[ \begin{array}{l}\begin{cases} x - 3 ≤ 0\\ x - 1 ≥ 0 \end{cases} \\\begin{cases} x ≤ 3 \\x ≥ 1 \end{cases} \end{array} \right.\)

`=> 1 ≤ x ≤ 3 `

Vậy ` S = { x | 1 ≤ x ≤ 3 } `

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$\text{@Bulletproof Boy Scout}$