Giải pt 2sqrt(x + 4) – 4sqrt(2x – 6) = x – 7

Đáp án:

`ĐKXĐ :  x ≥ 3`

Ta có

`2\sqrt{x + 4} – 4\sqrt{2x – 6} = x – 7`

`<=> 2\sqrt{x + 4} – 4\sqrt{2x – 6} – (x – 7) = 0`

`<=> (2\sqrt{x + 4} – 6) – (4\sqrt{2x – 6} – 8) – (x – 7 + 2) = 0`

`<=> 2(\sqrt{x + 4} – 3) – 4(\sqrt{2x – 6} – 2) – (x – 5) = 0`

`<=> 2 . (x + 4 – 9)/(\sqrt{x + 4} + 3) – 4 . (2x – 6 – 4)/(\sqrt{2x – 6} + 2) – (x – 5) = 0`

`<=> [2(x – 5)]/(\sqrt{x + 4} + 3) – [8(x – 5)]/(\sqrt{2x – 6} + 2) – (x – 5) = 0`

`<=> (x – 5)(2/(\sqrt{x + 4} + 3) – 8/(\sqrt{2x – 6} + 2) – 1) = 0`

`+) x – 5 = 0 <=> x = 5`

`+) 2/(\sqrt{x + 4} + 3) – 8/(\sqrt{2x – 6} + 2) – 1 = 0`

`<=> 2(\sqrt{2x – 6} + 2) – 8(\sqrt{x + 4} + 3) – (\sqrt{x + 4} + 3)(\sqrt{2x – 6} + 2) = 0`

`-> Vn_{o}`

Vậy `S = {5}`

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