Đáp án+Giải thích các bước giải:
a.
`sqrt(1-6x+9x) =8`
`<=> sqrt(1-3x) =8`
`<=> 1 + 3x =64`
`<=> 3x = 63`
`<=> x =21`
b.
`sqrt(1 + 6x^2 - 9x^4) = 8-x`
`<=> 1 + 6x^2 + 9x^4 = 64 - 16x + x^2`
`<=> -63 + 5x^2 + 9x^4 + 16x =0`
`<=> -63 - 21x^2 - x^2 + 27x^2 + 9x^4 + 7x + 9x + 3x^3 - 3x^3 =0`
`<=> 9(3x^2 + x -7) + 3x^2(3x^2 + x -7) - x (3x^2 + x -7)`
`<=> (3x^2 + x -7)(3x^2 -x +9)=0`
`<=>` $\left[ \begin{array}{l}3x^2 + x -7=0\\\\3x^2 - x + 9=0\end{array} \right. $
`<=>` $\left[ \begin{array}{l}x = \dfrac{-1 \pm \sqrt{1^2 -4 \times 3 \times(-7)}}{2\times3}\\\\x= \dfrac{-(-1)\pm \sqrt{(-1)^2 - 4\times 3 \times 9}}{2\times3}\end{array} \right.$
`<=>` $ \left[ \begin{array}{l}\left\{\begin{matrix} x= \dfrac{-1 + \sqrt{85}}{6}\\\\x= \dfrac{-1-\sqrt{85}}{6}\end{matrix}\right.\\x\notin \mathbb{R}\end{array} \right.$
c.
`sqrt(x^2 + 2 ) = 5-x`
`<=>x^2 + 2 = 25 - 10x + x^2`
`<=> 2 = 25 - 10x`
`<=> 10x = 23`
`<=> x = 23/10`
