`a)` `\sqrt{x}=13`
`<=>(\sqrt{x})^2=13^2`
`<=>x=169` `(TMĐK)`
Vậy `x=169`
`b)` `3\sqrt{x}=15`
`<=>\sqrt{x}=5`
`<=>(\sqrt{x})^2=5^2`
`<=>x=25` `(TMĐK)`
Vậy `x=25`
`c)` `2\sqrt{x}-1=5`
`<=>2\sqrt{x}=6`
`<=>\sqrt{x}=3`
`<=>(\sqrt{x})^2=3^2`
`<=>x=9` `(TMĐK)`
Vậy `x=9`
`d)` `5-3\sqrt{x}=2`
`<=>-3\sqrt{x}=2-5`
`<=>-3\sqrt{x}=-3`
`<=>\sqrt{x}=1`
`<=>x=1` `(TMĐK)`
Vậy `x=1`
`e)` `4x^2-9=0`
`<=>4x^2=9`
`<=>x^2=9/4`
`<=>x=±3/2`
`=>x=3/2` (do `-3/2<0)`
Vậy `x=3/2`
`f)` `21-3x^2=0`
`<=>-3x^2=-21`
`<=>x^2=7`
`<=>x=±\sqrt{7}`
`=>x=\sqrt{7}` (do `-\sqrt{7}<0)`
Vậy `x=\sqrt{7}`
`g)` `5x^2+6=0`
`<=>5x^2=-6` (vô lý vì `5x^2\geq0∀x;-6<0)`
Vậy phương trình trên vô nghiệm.
`h)` `5\sqrt{x}-2=3`
`<=>5\sqrt{x}=5`
`<=>\sqrt{x}=1`
`<=>x=1` `(TMĐK)`
Vậy `x=1`
`i)` `\sqrt{x}.(\sqrt{x}-1)=0`
`<=>` \(\left[ \begin{array}{l}\sqrt{x}=0\\\sqrt{x}-1=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=0\quad (\text{TMĐK})\\x=1\quad(\text{TMĐK})\end{array} \right.\)
Vậy `x=0;x=1`
`j)` `\sqrt{x}=8`
`<=>(\sqrt{x})^2=8^2`
`<=>x=64` `(TMĐK)`
Vậy `x=64`
`k)` `\sqrt{7x}=7`
`<=>(\sqrt{7x})^2=7^2`
`<=>7x=49`
`<=>x=7` `(TMĐK)`
Vậy `x=7`
`l)` `(\sqrt{x}-1)(\sqrt{x}-2)=0`
`<=>` \(\left[ \begin{array}{l}\sqrt{x}-1=0\\\sqrt{x}-2=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}\sqrt{x}=1\\\sqrt{x}=2\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=1\quad(\text{TMĐK})\\x=4\quad(\text{TMĐK})\end{array} \right.\)
`m)` `4\sqrt{x}-3=7`
`<=>4\sqrt{x}=10`
`<=>\sqrt{x}=5/2`
`<=>(\sqrt{x})^2=(5/2)^2`
`<=>x=25/4` `(TMĐK)`
Vậy `x=25/4`
`n)` `9-2\sqrt{x}=6`
`<=>-2\sqrt{x}=-3`
`<=>\sqrt{x}=3/2`
`<=>(\sqrt{x})^2=(3/2)^2`
`<=>x=9/4` `(TMĐK)`
Vậy `x=9/4`
