Đáp án+Giải thích các bước giải:
`a)`
`\sqrt{25x^2}-7=0`
`⇔\sqrt{(5x)^2}-7=0`
`⇔5|x|-7=0`
`⇔|x|=7/5`
\(⇔\left[ \begin{array}{l}x=\dfrac{7}{5}\\x=-\dfrac{7}{5}\end{array} \right.\)
Vậy `x∈{7/5;-7/5}`
`b)`
ĐK:`x>=0`
`x-2\sqrtx=0`
`⇔\sqrtx(\sqrtx-2)=0`
\(⇔\left[ \begin{array}{l}\sqrt x=0\\\sqrt x-2=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=0\\\sqrt x=2\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=0(TM)\\x=4(TM)\end{array} \right.\)
Vậy `x∈{0;4}`
`c)`
ĐK:`x>=0`
`x-3\sqrtx-4=0`
`⇔x-4\sqrtx+\sqrtx-4=0`
`⇔\sqrtx(\sqrtx-4)+(\sqrtx-4)=0`
`⇔(\sqrtx-4)(\sqrtx+1)=0`
\(⇔\left[ \begin{array}{l}\sqrt x-4=0\\\sqrt x+1=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}\sqrt x=4\\\sqrt x=-1(ktm)\end{array} \right.\)
`⇔\sqrtx=4`
`⇔x=16`
Vậy `x=16`
`d)`
`x^2-2\sqrt3x+3=0`
`⇔x^2-2.x.\sqrt3+(\sqrt3)^2=0`
`⇔(x-\sqrt3)^2=0`
`⇔x-\sqrt3=0`
`⇔x=\sqrt3`
Vậy `x=\sqrt3`
