Question

[Vũ Bảo Ngọc]

\(\frac{x+2}{5}=\frac{1}{x-2}\)                   \(\frac{X^2}{6}=\frac{24}{25}\)\(\frac{x}{3}=\frac{Y}{4}\)và x² +y²= 100

Answer 1

[Dương Lam Hàng]

a) Ta có: \(\frac{x+2}{5}=\frac{1}{x-2}\Leftrightarrow\left(x+2\right).\left(x-2\right)=5\)

                                              \(\Rightarrow x^2-4=5\)

                                              \(\Rightarrow x^2=9\)

                                              \(\Rightarrow x=\left\{3;-3\right\}\)

b) \(\frac{x^2}{6}=\frac{24}{25}\Rightarrow x^2=\frac{6.24}{25}=\frac{144}{25}\)

                            \(\Rightarrow x=\left\{\frac{12}{5};\frac{-12}{5}\right\}\)

c) \(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x^2}{3^2}=\frac{y^2}{4^2}=\frac{x^2+y^2}{3^2+4^2}=\frac{100}{25}=4\)

\(\Rightarrow x^2=4.9=36\Rightarrow x=\left\{-6;6\right\}\)

      \(y^2=4.16=64\Rightarrow y=\left\{-8;8\right\}\)

Answer 2

[Trắng_CV]

1 )           Ta có : 

\(\frac{x+2}{5}=\frac{1}{x-2}\)

\(\Rightarrow\left(x+2\right)\left(x-2\right)=1.5\)

\(\Rightarrow\left(x+2\right)x-\left(x+2\right).2=5\)

\(\Rightarrow x^2+2x-2x-4=5\)

\(\Rightarrow x^2-4=5\)

\(\Rightarrow x^2=5+4\)

\(\Rightarrow x^2=9\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)

Vậy ...

2 )          

\(\frac{x^2}{6}=\frac{24}{25}\Rightarrow x^2=\frac{24}{25}.6=\frac{144}{25}\Rightarrow\orbr{\begin{cases}x=\frac{12}{5}\\x=-\frac{12}{5}\end{cases}}\)

Vậy ...

3 )        

Ta có : 

\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}\)và      \(x^2+y^2=100\)

Áp dụng tính chất dãy tỉ số  bằng nhau , ta có : 

\(\frac{x^2}{9}=\frac{y^2}{16}=\frac{x^2+y^2}{9+16}=\frac{100}{25}=4\)

\(\Rightarrow\hept{\begin{cases}x^2=4.9=36\\y^2=4.16=64\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=\pm6\\y=\pm8\end{cases}}\)

Vậy ...