\(\left(5x+3\right)^3-\left(2x+4\right)^3=\left(3x-1\right)^3\)

\(\Leftrightarrow\left(5x+3\right)^3-\left(2x+4\right)^3-\left(3x-1\right)^3=0\)

\(\Leftrightarrow90x^3+204x^2+30x-36=0\)

\(\Leftrightarrow6\left(x+2\right)\left(3x-1\right)\left(5x+3\right)=0\)

\(\Leftrightarrow x\in\left\{-2;\frac{1}{3};\frac{-3}{5}\right\}\)

\(\left(5x+3\right)^3=\left(2x+4\right)^3+\left(3x-1\right)^3\)

Đặt 2x+4=a, 3x-1=b. ta có:

\(\left(a+b\right)^3=a^3+b^3\)

\(\Leftrightarrow a^3+b^3+3ab.\left(a+b\right)=a^3+b^3\)

\(\Leftrightarrow\orbr{\begin{cases}a=0\\b=0\end{cases}\text{hoặc }a=-b}\)

tự giải tiếp 

21/39=7/13

Trả lời 

\(\frac{21}{39}\)

\(=\frac{21:3}{39:3}\)

\(=\frac{7}{13}\)

Study well 

Ap dung BDT Bun-hia-cop-xki ta co:

\(\left(a.\cos\beta+b.\sin\beta\right)^2\le\left(a^2+b^2\right)\left(\cos^2\beta+\sin^2\beta\right)=a^2+b^2\)

\(\Rightarrow-\sqrt{a^2+b^2}\le a.\cos\beta+b.\sin\beta\le\sqrt{a^2+b^2}\)

Dau '=' xay ra khi \(\frac{a}{\cos\beta}=\frac{b}{\sin\beta}\)

                                                      Bài giải

\(\frac{58-m}{96+m}=\frac{5}{9}\)

\(9\left(58-m\right)=5\left(96+m\right)\)

\(522-9m=480+5m\)

\(9m-5m=522-480\)

\(4m=42\)

\(m=42\text{ : }4\)

\(m=\frac{21}{2}\)

                                                      Bài giải

\(\frac{58-m}{96+m}=\frac{5}{9}\)

\(9\left(58-m\right)=5\left(96+m\right)\)                     ( Nhân chéo )

\(522-9m=480+5m\)

\(9m-5m=522-480\)

\(4m=42\)

\(m=42\text{ : }4\)

\(m=\frac{21}{2}\)

\(A=\frac{\left(\frac{3}{5}-\frac{87}{200}+\frac{1}{200}\right):\left(-\frac{1}{25}\right)}{\frac{123}{4}+\frac{1}{12}+\frac{19}{6}}\)

\(A=\frac{\frac{17}{100}:\left(-\frac{1}{25}\right)}{34}\)

\(A=\frac{-\frac{17}{4}}{34}\)

\(A=\frac{-17}{4}.\frac{1}{34}\)

\(A=-\frac{1}{8}\)

Study well 

333 + 639 - 600 - 39 - 33 + 300 

= 972 - 600 - 39 - 33 + 300 

= 372 - ( 39 + 33 ) + 300

= 372 - 72 + 300

= 300 + 300

= 600

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