` a) ` ` x + 3\sqrt{x + 2} = 0 `
` <=> 3\sqrt{x + 2} = -x `
` <=> 9(x + 2) = x^2 `
` <=> 9x + 18 - x^2 = 0 `
` <=> -x^2 + 9x + 18 = 0 `
` <=> x^2 - 9x - 18 = 0 `
` <=> x = \frac{-(-9) ± \sqrt{(-9)^{2} - 4 . 1 . (-18)}}{2.1} `
` <=> x = \frac{9±\sqrt{153}}{2} `
` <=> x = \frac{9±3\sqrt{17}}{2} `
* Nếu ` x = \frac{9 + 3\sqrt{17}}{2} `
` <=> \frac{9 + 3\sqrt{17}}{2} + 3\sqrt{\frac{9+3\sqrt{17}}{2} + 2} = 0 `
` <=> 21,36932 = 0 ` `(vô` `lí)`
* Nếu ` x = \frac{9 - 3\sqrt{17}}{2} `
` <=> \frac{9 + 3\sqrt{17}}{2} + 3\sqrt{\frac{9+3\sqrt{17}}{2} + 2} = 0 `
` <=> 0 = 0 ` `(tm)`
` => x = \frac{9 - 3\sqrt{17}}{2} `
` b) ` ` x + \sqrt{x - 1} = 13 `
` <=> \sqrt{x - 1} = 13 - x `
` <=> x - 1 = 169 - 26x + x^{2} `
` <=> -x^{2} + 27x - 170 = 0 `
` <=> x^{2} - 27x + 170 = 0 `
` <=> x^{2} - 10x - 17x + 170 = 0 `
` <=> (x - 10)(x - 17) = 0 `
` <=> ` \(\left[ \begin{array}{l}x=10\\x=17\end{array} \right.\)
* Nếu ` x = 10 `
` <=> 10 + \sqrt{10 - 1} = 13 `
` <=> 13 = 13 ` `(tm) `
* Nếu ` x = 17 `
` <=> 17 + \sqrt{17 - 1} = 13 `
` <=> 21 = 13 ` `(vô` `lí)`
` => x = 10 `
