2 câu trả lời
Đáp án:
`2x - \sqrt{2x - 1} = 3`
`<=>\sqrt{2x -1} = 2x -3` `( ĐK : x≥ 3/2)`
`<=> 2x - 1= 4x^2 - 12x + 9`
`<=> - 4x^2 + 2x + 12x - 1 - 9 = 0`
`<=> - 4x^2 + 14x - 10 = 0`
`<=> 2x^2 - 7x + 5 = 0`
`<=> 2x^2 - 2x - 5x + 5 = 0`
`<=> 2x( x - 1) - 5( x -1)=0`
`<=> ( 2x -5)( x -1) = 0`
`<=>` \(\left[ \begin{array}{l}x=\frac{5}{2}(TM)\\x=1(KTM)\end{array} \right.\)
Vậy `S= { 5/2}`
Đáp án:
`2x-\sqrt{2x-1}=3`
`⇔ -\sqrt{2x-1} = 3 - 2x`
`⇔ \sqrt{2x-1} = -3 + 2x`
`⇔ \sqrt{2x-1} = 2x - 3(x ≥ 3/2)`
`⇔ 2x - 1 = (2x-3)^2`
`⇔ 2x - 1 = 4x^2 - 12x + 9`
`⇔ 2x - 1 - 4x^2 + 12x - 9 = 0`
`⇔ -4x^2 + 14x - 10 = 0`
`⇔ -4x^2 + 10x + 4x - 10 = 0`
`⇔ -4x^2 + 4x + 10x - 10 = 0`
`⇔ -4x(x-1)+10(x-1)=0`
`⇔ (x-1)(-4x+10)=0`
⇔\(\left[ \begin{array}{l}x=1(loại)\\x = \frac{5}{2}(nhận)\end{array} \right.\)
Vậy `S = {5/2}`
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