Question

Tìm x, y trong các tỉ lệ thức sau:

a) x - 3/x + 5

b) 7/x - 1 = x + 1/9

c) x + 4/20 = 5/x +4

d) x - 1/x+2 = x - 2/x + 3

Answer 1

a) Đề có bị thiếu không bạn?

b) \(\frac{7}{x-1}=\frac{x+1}{9}\)

\(\Rightarrow7.9=\left(x-1\right).\left(x+1\right)\)

\(\Rightarrow63=x^2+x-x-1\)

\(\Rightarrow63=x^2-1\)

\(\Rightarrow x^2=63+1\)

\(\Rightarrow x^2=64\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

Vậy \(x\in\left\{8;-8\right\}.\)

d) \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

\(\Rightarrow\left(x-1\right).\left(x+3\right)=\left(x-2\right).\left(x+2\right)\)

\(\Rightarrow x^2+3x-x-3=x^2+2x-2x-4\)

\(\Rightarrow x^2+2x-3=x^2-4\)

\(\Rightarrow x^2+2x-3-x^2+4=0\)

\(\Rightarrow2x+1=0\)

\(\Rightarrow2x=0-1\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=\left(-1\right):2\)

\(\Rightarrow x=-\frac{1}{2}\)

Vậy \(x=-\frac{1}{2}.\)

Chúc bạn học tốt!