\(\dfrac{x}{9}\) < \(\dfrac{4}{7}\) < \(x\) + \(\dfrac{1}{9}\)

\(\dfrac{7x}{63}\) < \(\dfrac{36}{63}\) < \(\dfrac{63x}{63}\) + \(\dfrac{7}{63}\)

7\(x\) < 36 < 63\(x\) + 7

⇒\(\left\{{}\begin{matrix}7x< 36\\63x+7>36\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x< \dfrac{36}{7}\\63x>36-7\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x< \dfrac{36}{7}\\63x>29\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x< \dfrac{36}{7}\\x>\dfrac{29}{63}\end{matrix}\right.\)

\(\dfrac{29}{63}\)<  \(x\) < \(\dfrac{36}{7}\) vì \(x\in\) Z nên \(x\in\) { 1; 2; 3; 4; 5}

⇒ \(\dfrac{x}{9}\) = \(\dfrac{1}{9}\); \(\dfrac{2}{9}\); \(\dfrac{3}{9}\); \(\dfrac{4}{9}\);\(\dfrac{5}{9}\)

a, 3⁶=3.3.3.3.3.3=729

6³=6.6.6=216

729>216 nên 3⁶>6³

b, 2²⁰⁰=2^2.100=(2²)¹⁰⁰=4¹⁰⁰

4¹⁰⁰=4¹⁰⁰ nên 4¹⁰⁰=2²⁰⁰

c, 333⁴⁴⁴=333^4.111=(333⁴)¹¹¹

444³³³=444^3.111=(444³)¹¹¹

Cả hai số đều cùng có số mũ 111 nên ta so sánh 333⁴ và 444³

333⁴=(3.111)⁴=3⁴.111⁴=81.111⁴

444³=(4.111)³=4³.111³=64.111³

81.111⁴>64.111³ nên 333⁴⁴⁴>444³³³

a, 3⁶ = (3²)³ = 9³ > 6³ vậy 3⁶ > 6³

Các câu khác làm như Lộc 

\(B=-\left(x+\dfrac{2}{5}\right)^2-\dfrac{5}{12}\le-\dfrac{5}{12}\left(-\left(x+\dfrac{2}{5}\right)^2\le0,\forall x\right)\)

\(\Rightarrow GTLN\left(B\right)=-\dfrac{5}{12}\)

B = -(\(x\) + \(\dfrac{2}{5}\))²  - \(\dfrac{5}{12}\)

Vì (\(x\) + \(\dfrac{2}{5}\))² ≥ 0

-(\(x+\dfrac{2}{5}\))² ≤ 0 ⇒ -(\(x+\dfrac{2}{5}\) )²- \(\dfrac{5}{12}\)  ≤ - \(\dfrac{5}{12}\)

B_max = - \(\dfrac{5}{12}\) ⇔ \(x\) = - \(\dfrac{2}{5}\)

\(-\dfrac{1}{2}=\dfrac{-1\times5}{2\times5}=-\dfrac{5}{10}\\ -\dfrac{1}{3}=\dfrac{-1\times5}{3\times5}=-\dfrac{5}{15}\\ -\dfrac{5}{10}>-\dfrac{5}{11};-\dfrac{5}{12};-\dfrac{5}{13};-\dfrac{5}{14}>-\dfrac{5}{15}\\ \Rightarrow a\in\left\{-\dfrac{5}{11};-\dfrac{5}{12};-\dfrac{5}{13};-\dfrac{5}{14}\right\}\)

-12 : (\(\dfrac{3}{4}\) - \(\dfrac{5}{6}\))²

= -12 : (-\(\dfrac{1}{12}\))²

= - 12³

= - 1728 

a) \(\left|x\right|-15=6\Rightarrow\left|x\right|=21\Rightarrow\left[{}\begin{matrix}x=21\\x=-21\end{matrix}\right.\)

b) \(\left|x\right|+4=0\Rightarrow\left|x\right|=-4\Rightarrow x\in\varnothing\)

c) \(x^2-16=0\Rightarrow x^2=16=4^2\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

a, /x/-15=6
    /x/     =6+15
   /x/      =21
   x        =\(\pm\)21
b, /x/+4=0

    /x/    =0-4
    /x/    =-4

    x      =4

c, x^2-16=0
   x^2       =0+16

   x^2       =16
   x^2        = (\(\pm\)4)^2
   x            =\(\pm\) 4

Chiều cao của mực nước là:

2,4 : 2 : 1,5 = 0,8 (m)

Kết luận:... 

\(\left(3x+2\right)\left(2x+9\right)-\left(x+2\right)\left(6x+1\right)=\left(x-1\right)-\left(x-6\right)\\ \Leftrightarrow6x^2+31x+18-6x^2-13x-2=x-1-x+6\\ \Leftrightarrow18x+16=5\\ \Leftrightarrow18x=-11\\ \Leftrightarrow x=-\dfrac{11}{18}\)