Đáp án:
Giải thích các bước giải:
`a)`
ĐKXĐ : `x \ge 0`
`sqrt{x-5}=3`
`⇔ (sqrt{x-5})^2 = 3^2`
`⇔ x - 5 = 9`
`⇔ x = 14(TM)`
`b)`
ĐKXĐ : `x \le 4/5`
`sqrt{4-5x} = 12`
`⇔ (sqrt{4-5x})^2 = 12^2`
`⇔ 4 - 5x = 144`
`⇔ -5x = 140`
`⇔ x = -28(TM)`
`c)`
ĐKXĐ : `x \le 6`
`\sqrt{6-x} = 3x - 4`
`⇔ (sqrt{6-x})^2 = (3x-4)^2`
`⇔ 6 - x = 9x^2 - 24x + 16`
`⇔ 9x^2 - 23x + 10 = 0`
`⇔ (9x^2-5x)+(-18x+10)=0`
`⇔ x(9x-5) - 2(9x-5) = 0`
`⇔ (x-2)(9x-5) =0`
`⇔`\(\left[ \begin{array}{l}x-2=0\\9x-5=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=2(TM)\\x=\dfrac59(TM)\end{array} \right.\)
`d)`
ĐKXĐ : `x \le 5`
`sqrt{5-x} = 9 - 2x`
`⇔ (sqrt{5-x})^2 = (9-2x)^2`
`⇔ 5 -x = 81 - 36x + 4x^2`
`⇔ 4x^2 - 35x + 76 = 0`
`⇔ (4x^2-16x) + (-19x+76) =0`
`⇔ 4x(x-4) - 19(x-4) = 0`
`⇔ (x-4)(4x-19)=0`
`⇔`\(\left[ \begin{array}{l}x-4=0\\4x-19=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=4(TM)\\x=\dfrac{19}4(TM)\end{array} \right.\)
