giải pt :3√x-1 + √9x-9 – √25x-25 + 2√4x-4 =24 06/07/2021 Bởi aihong giải pt :3√x-1 + √9x-9 – √25x-25 + 2√4x-4 =24
`3sqrt{x – 1} + sqrt{9x – 9} – sqrt{25x – 25} + 2sqrt{4x – 4} = 24` `(ĐK: x >= 1)` `<=> 3sqrt{x – 1} + 3sqrt{x – 1} – 5sqrt{x – 1} + 4sqrt{x – 1} = 24` `<=> 5sqrt{x – 1} = 24` `<=> sqrt{x – 1} = 24/5` `<=> x – 1 = 576/25` `<=> x = 601/25` Bình luận
Đáp án: $x = \dfrac{601}{25}$ Giải thích các bước giải: $3\sqrt{x – 1} + \sqrt{9x -9} – \sqrt{25x – 5} + 2\sqrt{4x – 4} = 24$ $(*)$ $ĐK:\, x \geq 1$ $(*) 3\sqrt{x – 1} + \sqrt{9(x -1)} – \sqrt{25(x – 1)} + 2\sqrt{4(x – 1)} = 24$ $\Leftrightarrow 3\sqrt{x – 1} + 3\sqrt{x – 1} – 5\sqrt{x – 1} + 4\sqrt{x – 1} = 24$ $\Leftrightarrow 5\sqrt{x – 1} = 24$ $\Leftrightarrow \sqrt{x – 1} = \dfrac{24}{5}$ $\Rightarrow x – 1 = \dfrac{576}{25}$ $\Rightarrow x = \dfrac{601}{25}$ (nhận) Vậy $x = \dfrac{601}{25}$ Bình luận
`3sqrt{x – 1} + sqrt{9x – 9} – sqrt{25x – 25} + 2sqrt{4x – 4} = 24` `(ĐK: x >= 1)`
`<=> 3sqrt{x – 1} + 3sqrt{x – 1} – 5sqrt{x – 1} + 4sqrt{x – 1} = 24`
`<=> 5sqrt{x – 1} = 24`
`<=> sqrt{x – 1} = 24/5`
`<=> x – 1 = 576/25`
`<=> x = 601/25`
Đáp án:
$x = \dfrac{601}{25}$
Giải thích các bước giải:
$3\sqrt{x – 1} + \sqrt{9x -9} – \sqrt{25x – 5} + 2\sqrt{4x – 4} = 24$ $(*)$
$ĐK:\, x \geq 1$
$(*) 3\sqrt{x – 1} + \sqrt{9(x -1)} – \sqrt{25(x – 1)} + 2\sqrt{4(x – 1)} = 24$
$\Leftrightarrow 3\sqrt{x – 1} + 3\sqrt{x – 1} – 5\sqrt{x – 1} + 4\sqrt{x – 1} = 24$
$\Leftrightarrow 5\sqrt{x – 1} = 24$
$\Leftrightarrow \sqrt{x – 1} = \dfrac{24}{5}$
$\Rightarrow x – 1 = \dfrac{576}{25}$
$\Rightarrow x = \dfrac{601}{25}$ (nhận)
Vậy $x = \dfrac{601}{25}$