`@` `\text {Ans}`

`\downarrow`

`a)`

`-9/34*17/4`

`=`\(\dfrac{-9}{17\cdot2}\cdot\dfrac{17}{4}\)

`=`\(-\dfrac{9}{2}\cdot\dfrac{1}{4}\)

`=`\(-\dfrac{9}{8}\)

`b)`

\(\dfrac{17}{15}\div\dfrac{4}{3}\)

`=`\(\dfrac{17}{15}\cdot\dfrac{3}{4}\)

`=`\(\dfrac{17}{3\cdot5}\cdot\dfrac{3}{4}\)

`=`\(\dfrac{17}{5}\cdot\dfrac{1}{4}\)

`=`\(\dfrac{17}{20}\)

`c)`

\(4\dfrac{1}{5}\div\left(-2\dfrac{4}{5}\right)\)

`=`\(4\dfrac{1}{5}\cdot\left(-\dfrac{5}{14}\right)\)

`=`\(\dfrac{21}{5}\cdot\left(-\dfrac{5}{14}\right)\)

`=`\(-\dfrac{21}{14}=-\dfrac{3}{2}\)

a) \(\dfrac{-9}{34}\cdot\dfrac{17}{4}\)

\(=\dfrac{-9\cdot17}{34\cdot4}\)

\(=-\dfrac{153}{136}\)

\(=\dfrac{9}{8}\)

b) \(\dfrac{17}{15}:\dfrac{4}{3}\)

\(=\dfrac{17}{15}\cdot\dfrac{3}{4}\)

\(=\dfrac{17\cdot3}{15\cdot4}\)

\(=\dfrac{51}{60}=\dfrac{17}{20}\)

c) \(4\dfrac{1}{5}:\left(-2\dfrac{4}{5}\right)\)

\(=\dfrac{21}{5}:-\dfrac{14}{5}\)

\(=\dfrac{21}{5}\cdot-\dfrac{5}{14}\)

\(=\dfrac{21\cdot-5}{5\cdot14}\)

\(=-\dfrac{105}{70}=\dfrac{3}{2}\)

a) −934⋅17434−9​⋅417​

=−9⋅1734⋅4=34⋅4−9⋅17​

=−153136=−136153​

=98=89​

b) 1715:431517​:34​

=1715⋅34=1517​⋅43​

=17⋅315⋅4=15⋅417⋅3​

=5160=1720=6051​=2017​

c) 415:(−245)451​:(−254​)

=215:−145=521​:−514​

=215⋅−514=521​⋅−145​

=21⋅−55⋅14=5⋅1421⋅−5​

=−10570=32=−70105​=23​
 

a: \(=703-140:\left(38+32\right)-17^{15}:17^{13}\)

\(=703-140:70-17^2\)

\(=701-289=412\)

b: \(=1024:32+140:\left(38+32\right)+23^2-7^2\)

\(=32+140:70+529-49\)

\(=32+4+480=516\)

c: \(=17^4\cdot17:17^3-14\cdot4:8\)

\(=17^2-7=289-7=282\)

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

17⁵+24⁴-13²¹

=17⁴.17+(...6)-13²⁰.13

=17⁴.17+(...6)-(13⁴)⁵.13

=(...7)+(...6)-(...3)

=...0

=> 17⁵+24⁴-13²¹\(⋮\)10

vậy..

Tại sao (13^4)^5 x 13 lại có chữ số tân cùng =3

vì 13²¹​ có tận cùng là 3. bn xem lại sẽ rõ

\(2,\\ a,\sqrt{4x-4}+\sqrt{9x-9}-\sqrt{25x-25}=7\left(x\ge1\right)\\ \Leftrightarrow2\sqrt{x-1}+3\sqrt{x-1}-5\sqrt{x-1}=7\\ \Leftrightarrow0\sqrt{x-1}=7\Leftrightarrow x\in\varnothing\\ b,\sqrt{2x^2-3}=4\left(x\le-\dfrac{\sqrt{6}}{2};\dfrac{\sqrt{6}}{2}\le x\right)\\ \Leftrightarrow2x^2-3=16\\ \Leftrightarrow x^2=\dfrac{19}{2}\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{19}{2}}\left(tm\right)\\x=-\sqrt{\dfrac{19}{2}}\left(tm\right)\end{matrix}\right.\)

\(1,\\ A=\sqrt{5+4x}+\sqrt{7-3x}\\ ĐKXĐ:\left\{{}\begin{matrix}5+4x\ge0\\7-3x\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{5}{4}\\x\le\dfrac{7}{3}\end{matrix}\right.\)

Bài 2:

a) \(\sqrt{4x-4}+\sqrt{9x-9}-\sqrt{25x-25}=7\left(đk:x\ge1\right)\)

\(\Leftrightarrow2\sqrt{x-1}+3\sqrt{x-2}-5\sqrt{x-1}=7\)

\(\Leftrightarrow0=7\left(VLý\right)\)

Vậy \(S=\varnothing\)

b) \(\sqrt{2x^2-3}=4\left(đk:-\sqrt{\dfrac{3}{2}}\ge x\ge\sqrt{\dfrac{3}{2}}\right)\)

\(\Leftrightarrow2x^2-3=16\)

\(\Leftrightarrow2x^2=19\Leftrightarrow x^2=\dfrac{19}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{19}{2}}\left(tm\right)\\x=-\sqrt{\dfrac{19}{2}}\left(tm\right)\end{matrix}\right.\)

Mình cần gấp nha mn 😭😭 

1) Ta có: \(\frac{x+6\sqrt{x}+9}{x-9}=\frac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\sqrt{x}-3}\)

Ms bt lm 1 thoii

\(\frac{x+6\sqrt{x}+9}{x-9}=\frac{\left(\sqrt{x}\right)^2+2.3.\sqrt{x}+3^2}{\left(\sqrt{x}\right)^2-3^2}=\frac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\sqrt{x}-3}\)

còn 2 ch nghí ra!

\(\frac{9}{2}\) \(-\) (  \(x\) \(-\) \(\frac{3}{4}\) )   =  \(\frac{25}{4}\)

                      \(x\) \(-\) \(\frac{3}{4}\)      =   \(\frac{9}{2}\) \(-\) \(\frac{25}{4}\)

                      \(x\)  \(-\) \(\frac{3}{4}\)    =  \(-\frac{7}{4}\)

                                   \(x\)           =    \(-\frac{7}{4}\) \(+\)  \(\frac{3}{4}\) 

                                   \(x\)           =      \(-1\)

\(4\) \(+\) \(x\) \(+\) \(\frac{3}{4}\)     =  \(\frac{17}{2}\)

(  \(4\) \(+\) \(\frac{3}{4}\))  \(+\)\(x\) =     \(\frac{17}{2}\)

      \(\frac{19}{4}\)      \(+\)    \(x\)      =      \(\frac{17}{2}\)

                                 \(x\)         =    \(\frac{17}{2}\) \(-\)    \(\frac{19}{4}\) 

                               \(x\)          =  \(\frac{15}{4}\)

\(\frac{5}{7}\) \(+\) \(\frac{4}{5}\) \(-\) \(x\) =  \(\frac{9}{7}\)

     \(\frac{53}{35}\)  \(-\)  \(x\)           =   \(\frac{9}{7}\)

                         \(x\)               =   \(\frac{53}{35}\) \(-\) \(\frac{9}{7}\)

                        \(x\)                =     \(\frac{8}{35}\)

-  Hok T - 

Phân tích ra thừa số nguyên tố

`4=2^2`

`9=3^2`

`53=53`

`36=2^2 *3^2`

`=>BCNNN=2^2 *3^2 *53=1908`

`3/4+1/9+(-1/53)+5/36`

`=1431/1908+212/1908-36/1908+265/1908`

`=1872/1908=52/53`