a) \(\frac{x-1}{6}=\frac{2x+3}{7}\)

\(\Leftrightarrow7\left(x-1\right)=6\left(2x+3\right)\)

\(\Leftrightarrow7x-7=12x+18\)

\(\Leftrightarrow5x+18=-7\)

\(\Leftrightarrow5x=-25\)

\(\Leftrightarrow x=-5\)

b) \(\left(2x^2-\frac{1}{2}x\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow x\left(2x-\frac{1}{2}\right)\left(x^2+1\right)=0\)

Vì \(x^2+1>0\)nên \(\orbr{\begin{cases}x=0\\2x-\frac{1}{2}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{4}\end{cases}}\)

x chia hết cho 5 và 2 hả bn?

Ta có : \(\hept{\begin{cases}x⋮5\\x⋮2\end{cases}}\Rightarrow x\in BC\left(2;5\right)\)

Lại có : BCNN(2;5) = 2.5 = 10

mà BC(2;5) = B(10) = {0;10;20;30;40;50;60;70;80;90;100...}

Vì x < 90

=> x \(\in\){0;10;20;30;40;50;60;70;80}

Câu hỏi của Sunnyy - Toán lớp 7 - Học toán với OnlineMath

Tham khảo

Vì \(\left|y-\frac{1}{3}\right|\ge0\)

\(\Rightarrow\frac{2}{7}\left|y-\frac{1}{3}\right|\ge0\)

\(\Rightarrow-\frac{2}{7}\left|y-\frac{1}{3}\right|\le0\)

hay \(B\le0\)

Vậy \(GTLN_B=0\), dấu bằng xảy ra khi \(y=\frac{1}{3}\)

\(a,\frac{x-1}{12}=\frac{75}{x-1}\)

\(\Rightarrow\left(x-1\right)\left(x-1\right)=12\cdot75\)

\(\Rightarrow\left(x-1\right)^2=900\)

\(\Rightarrow x-1=\pm30\)

\(\Rightarrow\orbr{\begin{cases}x=31\\x=-29\end{cases}}\)

\(b,\left|12-|4x+1|\right|=5\)

\(\Rightarrow\orbr{\begin{cases}12-\left|4x+1\right|=5\\12-\left|4x+1\right|=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\left|4x+1\right|=7\\\left|4x+1\right|=17\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}4x+1=7\text{ hoặc}4x+1=-7\\4x+1=17\text{ hoặc}4x+1=-17\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}or\text{ }x=-2\\x=4or\text{ }x=-\frac{9}{2}\end{cases}}\)

x - 1/12 = 75/x - 1

<=> (x - 1).(x - 1) = 12.75

<=> x² - 2x + 1 = 900

<=> x² - 2x + 1 - 900 = 0

<=> x² - 2x + 1 - 899 = 0

<=> (x + 29)(x - 31) = 0

        x + 29 = 0 hoặc x - 31 = 0

        x = 0 - 29          x = 0 + 31

        x = -29              x = 31

=> x = -29 hoặc x = 31

\(A=\frac{5x+4}{3x-1}>0\)

\(\Leftrightarrow\hept{\begin{cases}5x+4>0\\3x-1>0\end{cases}}\) hoặc \(\hept{\begin{cases}5x+4< 0\\3x-1< 0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}5x>-4\\3x>1\end{cases}}\) hoặc \(\hept{\begin{cases}5x< -4\\3x< 1\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x>-\frac{4}{5}\\x>\frac{1}{3}\end{cases}}\) hoặc \(\hept{\begin{cases}x< -\frac{4}{5}\\x< \frac{1}{3}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>\frac{1}{3}\\x< -\frac{4}{5}\end{cases}}\)

b, tương tự nhưng xét trái dấu

Để mình giải câu b) cho \(A< 0\Leftrightarrow\frac{5x+4}{3x-1}< 0\)

\(\Leftrightarrow\hept{\begin{cases}5x+4>0\\3x-1< 0\end{cases}}\)hoặc \(\hept{\begin{cases}5x+4< 0\\3x-1>0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}5x>-4\\3x< 1\end{cases}}\)hoặc \(\hept{\begin{cases}5x< -4\\3x>1\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x>\frac{-4}{5}\\x< \frac{1}{3}\end{cases}}\left(TM\right)\)hoặc \(\Leftrightarrow\hept{\begin{cases}x< \frac{-4}{5}\\x>\frac{1}{3}\end{cases}}\left(L\right)\)

Vậy \(A< 0\Leftrightarrow\frac{-4}{5}< x< \frac{1}{3}\)

5³ . 5⁵ . 25 = 5³ . 5⁵ . 5² = 5^{3 + 5 + 2} = 5¹⁰

7⁴ . 7 . 49 = 7⁴ . 7¹ . 7² = 7^{4 + 1 + 2} = 7⁷

=))

\(5^3.5^5.25=5^3.5^5.5^2\)

                \(=5^{10}\)

  \(7^4.7.49=7^4.7.7^2\)

                \(=7^7\)

Rất vui vì giúp đc bạn <3

dẻ vạy mà kh biết 

\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)

= \(\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)

= \(\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

= \(\frac{1}{5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

= \(\frac{1}{5}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

= \(\frac{1}{5}.\left(1-\frac{1}{6}\right)\)

= \(\frac{1}{5}.\frac{5}{6}\)

= \(\frac{1}{6}\)

\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)

\(=\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)

\(=\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

\(=\frac{1}{10}.2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

\(=\frac{1}{10}.2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{6}\right)\)

\(=\frac{1}{5}.\frac{5}{6}\)

\(=\frac{1}{6}\)

Rất vui vì giúp đc bạn <3

BÀI 1 là 16 x 17 x 18 x 19

BÀI 2 KHÔNG BIẾT

BÀI 2 : Rơi vào thứ tư