Áp dụng bất đẳng thức AM - GM:

\(\sqrt{\left(x^2-15\right)\left(x-3\right)}\le\dfrac{x^2-15+x-3}{2}=\dfrac{x^2+x-18}{2};\sqrt{x^2-15}\le\dfrac{x^2-15+1}{2}=\dfrac{x^2-14}{2};\sqrt{x-3}\le\dfrac{x-3+1}{2}=\dfrac{x-2}{2}\).

Do đó \(F\ge x^2+x-\dfrac{x^2+x-18}{2}-\dfrac{x^2-14}{2}-\dfrac{x-2}{2}-38=-21\).

Đẳng thức xảy ra khi x = 4.

Vậy...

75 nhé bạn

TL :

   ( 15 x 15 ) : 2 x ( 15 x 15 ) : 2 x ( 15 x 15 ) : 2 + ( 0 + 1 + 2 + 2 + 3 + 45 ) x 0

= 0

=> vì : tất cả số nào nhân vs 0 đều = 0

_HT_

1423828.125 

        - ht -

1.

b) \(3^x+3^{x+2}=2430\)

\(\Rightarrow3^x.1+3^x.3^2=2430\)

\(\Rightarrow3^x.\left(1+3^2\right)=2430\)

\(\Rightarrow3^x.10=2430\)

\(\Rightarrow3^x=2430:10\)

\(\Rightarrow3^x=243\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\)

Vậy \(x=5.\)

c) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)

\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)

\(\Rightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=15\\2x-15=\pm1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=15:2\\2x-15=1\\2x-15=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\2x=16\\2x=14\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\x=8\\x=7\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{15}{2};8;7\right\}.\)

Chúc bạn học tốt!

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:>?

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`@` `\text {Ans}`

`\downarrow`

`a)`

`x + 10 = 20`

`=> x = 20 -10`

`=> x = 10`

Vậy, `x = 10`

`b)`

`2 * x + 15 = 35`

`=> 2x = 35 - 15`

`=> 2x = 20`

`=> x = 20 \div 2`

`=> x = 10`

Vậy, `x = 10`

`c)`

`3 * ( x + 2 ) = 15`

`=> x + 2 = 15 \div 3`

`=> x + 2 = 5`

`=> x = 5 - 2`

`=> x = 3`

Vậy, `x = 3`

`d)`

`10 * x + 15 * 11 = 20 * 10`

`=> 10x + 165 = 200`

`=> 10x = 200 - 165`

`=> 10x = 35`

`=> x = 35 \div 10`

`=> x = 3,5`

Vậy,` x = 3,5`

`e)`

`4 * ( x + 2 ) = 3 * 4`

`=> x + 2 = 12 \div 4`

`=> x + 2 = 3`

`=> x = 3 - 2`

`=> x = 1`

Vậy,` x = 1`

`f)`

`33 x + 135 = 26 * 9`

`=> 33x + 135 = 234`

`=> 33x = 234 - 135`

`=> 33x = 99`

`=> x = 99 \div 33`

`=> x = 3`

Vậy, `x = 3`

`g)`

`2 * x + 15 + 16 + 17 = 100`

`=> 2x + 48 = 100`

`=> 2x = 100 - 48`

`=> 2x = 52`

`=> x = 52 \div 2`

`=> x =26`

`h)`

`2 * (x + 9 + 10 + 11) = 4 . 12 . 25`

`=> 2 * (x + 9 + 10 + 11) = 4*25*12`

`=> 2 * (x + 9 + 10 + 11) = 100*12`

`=> x + 9 + 10 + 11 = 100*12 \div 2`

`=> x + 30 = 600`

`=> x = 600 - 30`

`=> x = 570`

Vậy, `x = 570.`

a) \(x+10=20\Leftrightarrow x=10\)

b) \(2x+15=35\Leftrightarrow2x=20\Leftrightarrow x=10\)

c) \(3.\left(x+2\right)=15\Leftrightarrow x+2=5\Leftrightarrow x=3\)

d) \(10x+15.11=20.10\Leftrightarrow10x+165=200\Leftrightarrow10x=35\Leftrightarrow x=\dfrac{35}{10}=\dfrac{7}{2}\)

e) \(4.\left(x+2\right)=3.4\Leftrightarrow x+2=3\Leftrightarrow x=1\)

f) \(35x+135=26.9\Leftrightarrow35x=234-135\Leftrightarrow35x=99\Leftrightarrow x=\dfrac{99}{35}\)

g) \(2x+15+16+17=100\Leftrightarrow2x+48=100\Leftrightarrow2x=52\Leftrightarrow x=26\)

h) \(2.\left(x+9+10+11\right)=4.12.25\)

\(\Leftrightarrow x+30=2.12.25\)

\(\Leftrightarrow x=600-30\)

\(\Leftrightarrow x=570\)

\(1,\frac{2}{3}+\frac{4}{9}+\frac{1}{5}+\frac{2}{15}+\frac{3}{2}-\frac{17}{18}\)

\(< =>\frac{4}{9}+\frac{3}{2}+\left(\frac{2}{3}+\frac{1}{5}+\frac{2}{15}\right)-\frac{17}{18}\)

\(< =>\frac{8}{18}+\frac{27}{18}+\left(\frac{10}{15}+\frac{3}{15}+\frac{2}{15}\right)-\frac{17}{18}\)

\(< =>\frac{35}{18}+1-\frac{17}{18}\)

\(< =>\frac{53}{18}-\frac{17}{18}\)

\(< =>2\)

\(2,\frac{13}{28}\cdot\frac{5}{12}-\frac{5}{28}\cdot\frac{1}{12}\)

\(< =>\left(\frac{13}{28}-\frac{5}{28}\right)\cdot\left(\frac{5}{12}-\frac{1}{12}\right)\)

\(< =>\frac{2}{7}\cdot\frac{1}{3}\)

\(< =>\frac{2}{21}\)

\(3,\frac{19}{4}\cdot\frac{15}{23}-\frac{15}{4}\cdot\frac{7}{23}+\frac{15}{4}\cdot\frac{11}{23}\)

\(< =>\frac{285}{92}-\frac{105}{92}+\frac{165}{92}\)

\(< =>\frac{15}{4}\)

cảm ơn bạn nha bạn chắc chăn đúng không

bạn viết dấu gạch ngang của phân số như thế nào đấy nguyen thi hien

a,     (\(\dfrac{9}{10}\) - \(\dfrac{15}{16}\)) \(\times\) ( \(\dfrac{5}{12}\) - \(\dfrac{11}{15}\) - \(\dfrac{7}{20}\))

=  (\(\dfrac{72}{80}\) - \(\dfrac{75}{80}\))  \(\times\) (\(\)\(\dfrac{25}{60}\) - \(\dfrac{44}{60}\)  - \(\dfrac{21}{60}\))

= - \(\dfrac{3}{80}\)  \(\times\) (- \(\dfrac{2}{3}\))

= \(\dfrac{1}{40}\) 

b, (-1)³ + (- \(\dfrac{2}{3}\))² : 2\(\dfrac{2}{3}\) + \(\dfrac{5}{6}\)

=  -1³ +   \(\dfrac{4}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{5}{6}\)

= -1 + \(\dfrac{4}{9}\) \(\times\) \(\dfrac{3}{8}\) + \(\dfrac{5}{6}\)

= -1 + \(\dfrac{1}{6}\) + \(\dfrac{5}{6}\)
= -1 + 1

= 0

c, 15 \(\times\) (- \(\dfrac{1}{5}\))² + \(\dfrac{1}{5}\) - 2 \(\times\) (- \(\dfrac{1}{2}\))³ - \(\dfrac{1}{2}\)

= 15 \(\times\) \(\dfrac{1}{25}\) + \(\dfrac{1}{5}\) - 2 \(\times\) (- \(\dfrac{1}{8}\)) - \(\dfrac{1}{2}\)

=  \(\dfrac{3}{5}\)  + \(\dfrac{1}{5}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{2}\)

= \(\dfrac{4}{5}\) - \(\dfrac{1}{4}\)

= \(\dfrac{11}{20}\)

a

\(x^2\left(2x+15\right)+4\left(2x+15\right)=0\\ \Leftrightarrow\left(2x+15\right)\left(x^2+4\right)=0\\ \Leftrightarrow2x+15=0\left(x^2+4>0\forall x\right)\\ \Leftrightarrow2x=-15\\ \Leftrightarrow x=-\dfrac{15}{2}\)

b

\(5x\left(x-2\right)-3\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(5x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\5x-3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0+2=2\\x=\dfrac{0+3}{5}=\dfrac{3}{5}\end{matrix}\right.\)

c

\(2\left(x+3\right)-x^2-3x=0\\ \Leftrightarrow2\left(x+3\right)-\left(x^2+3x\right)=0\\ \Leftrightarrow2\left(x+3\right)-x\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(2-x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\2-x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0-3=-3\\x=2-0=2\end{matrix}\right.\)

a: =>(2x+15)(x^2+4)=0

=>2x+15=0

=>2x=-15

=>x=-15/2

b; =>(x-2)(5x-3)=0

=>x=2 hoặc x=3/5

c: =>(x+3)(2-x)=0

=>x=2 hoặc x=-3

hộ mik nha

a)\(2.x-\frac{3}{2}=\frac{1}{2}\)

\(2x=\frac{4}{2}\)

\(x=\frac{4}{2}:2\)

\(x=1\)

Vậy x=1

b)\(\frac{8}{13}.x+\frac{5}{13}.x=\frac{1}{10}\)

\(x.\left(\frac{8}{13}+\frac{5}{13}\right)=\frac{1}{10}\)\

\(x.1=\frac{1}{10}\)

\(x=\frac{1}{10}\)

Vậy x=\(\frac{1}{10}\)

c)\(\frac{2}{15}+\frac{7}{15}.x=\frac{1}{15}\)

\(\frac{7}{15}x=\frac{-1}{15}\)

x=\(\frac{-1}{7}\)

Vậy \(x=\frac{-1}{7}\)

\(\frac{3}{2}\cdot x-\frac{3}{2}=\frac{1}{2}\)                           \(\frac{8}{13}\cdot x+\frac{5}{13}\cdot x=\frac{1}{10}\)

\(\frac{3}{2}\cdot x=\frac{3}{2}+\frac{1}{2}=2\)                    \(\left[\frac{8}{13}+\frac{5}{13}\right]\cdot x=\frac{1}{10}\)

\(x=2:\frac{3}{2}\)                                            \(1\cdot x=\frac{1}{10}\)

x=\(\frac{4}{3}\)                                                     \(x=\frac{1}{10}:1\)

Vậy x=\(\frac{4}{3}\)                                               \(x=\frac{1}{10}\)

                                                             Vậy x=\(\frac{1}{10}\)

c,\(\frac{2}{5}+\frac{7}{15}\cdot x=\frac{1}{15}\)

\(\frac{7}{15}\cdot x=\frac{1}{15}-\frac{2}{5}=\frac{-1}{3}\)

\(x=\frac{-1}{3}:\frac{7}{15}\)

\(x=\frac{-5}{7}\)

Vậy x=\(\frac{-5}{7}\)