`sqrt{81} + 6 sqrt{25} - 5`
`= 9 + 6 . 5 - 5 `
`= 9 + 30 - 5`
`= 34`
`7sqrt{48} + 4sqrt{27/16} - 15/sqrt{3}`
`= 28sqrt{3} + 3sqrt{3} - 5sqrt{3}`
`= (28 + 3 - 5) sqrt{3} `
`= 26 sqrt{3}`
`1/(2-sqrt{3}) + 3/(sqrt{3} + sqrt{2}) - 3 sqrt{(sqrt{3} - 1)^2}`
`= (2+sqrt{3})/(4-3) + (3(sqrt{3} - sqrt{2}))/(3-2) - 3 |sqrt{3} - 1|`
`= (2+sqrt{3})/1 + (3(sqrt{3} - sqrt{2}))/1 - 3 (sqrt{3} - 1)`
`= 2+sqrt{3} + 3sqrt{3} - 3sqrt{2} - 3 sqrt{3} + 3`
`= 5 - 3sqrt{2} + sqrt{3}`
\(\sqrt{x-3}=2\left(đk:x\ge3\right)\)
\(\Rightarrow x-3=4
\)
\(\Rightarrow x=7\) (thoả mãn)
Vậy
\(\sqrt{9x^2-6x+1}=5\left(9x^2-6x+1\ge0\forall x\right)\)
\(\Rightarrow\sqrt{\left(3x-1\right)^2}=5\)
\(\Rightarrow\left|3x-1\right|=5\)
\(\Rightarrow\left[{}\begin{matrix}3x-1=5\\3x-1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=6\\3x=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\)
`sqrt{x-3} = 2 (x >=3)`
`<=> x - 3 = 4`
`<=> x = 7` (Thỏa mãn)
Vậy `x = 7`
`sqrt{9x^2 - 6x + 1} = 5 `
`ĐKXĐ: 9x^2 - 6x + 1 >=0 <=> (3x - 1)^2 >= 0 `
`<=> 9x^2 - 6x + 1 = 25 `
`<=> 9x^2 - 6x - 24 = 0`
`<=> (x - 2)(3x + 4) = 0`
`<=> x = 2` hoặc `x = -3/4`
Vậy ...
