bài 1 tìm x,y,z
a, \(\dfrac{x}{10}\)=\(\dfrac{y}{15}\),x=\(\dfrac{7}{2}\) và x +2y-3z=20
b,2x=3y,49=57 và 4x-3y+5z=7
c, \(\dfrac{2x}{3}\)=\(\dfrac{3y}{4}\)=\(\dfrac{47}{5}\) và x+y+z=49
bài 2 tìm x trong tỉ lệ thức sau
a, \(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)
b,\(\dfrac{7}{x-1}\) =\(\dfrac{x+1}{9}\)
c,\(\dfrac{x+4}{20}=\dfrac{2}{x+4}\)
d,\(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)
Bài 2: a) \(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)
\(\Leftrightarrow\left(x-3\right).7=\left(x+5\right).5\)
\(\Leftrightarrow7x-21=5x+25\)
\(\Leftrightarrow7x-5x=21+25\)
\(\Leftrightarrow2x=46\)
\(\Rightarrow x=46:2=23\)
b) \(\dfrac{7}{x-1}=\dfrac{x+1}{9}\)
\(\Leftrightarrow\left(x+1\right)\left(x-1\right)=63\)
\(\Leftrightarrow x^2-1=63\)
\(\Leftrightarrow x^2=64\)
\(\Rightarrow x^2=\left(\pm8\right)^2\)
\(\Rightarrow x=8\) hoặc \(x=-8\)
2)a) \(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)
\(\Leftrightarrow7\left(x-3\right)=5\left(x+5\right)\)
\(7x-21=5x+25\)
\(7x-5x+25=21\)
\(2x+25=21\)
\(2x=-4\Rightarrow x=-2\)
b) \(\dfrac{7}{x-1}=\dfrac{x+1}{9}\)
\(7.9=\left(x+1\right)\left(x-1\right)\)
\(63=x\left(x-1\right)+1\left(x-1\right)\)
\(63=x^2-x+x-1\)
\(x^2=63+1=64\)
\(x=\left\{\pm8\right\}\)
c) \(\dfrac{x+4}{20}=\dfrac{2}{x+4}\)
\(\Leftrightarrow\left(x+4\right)\left(x+4\right)=2.20=40\)
\(x\left(x+4\right)+4\left(x+4\right)=40\)
\(x^2+4x+4x+16=40\)
\(x^2+8x=40-16=24\)
\(x\left(x+8\right)=24\)
\(x\in\left\{\varnothing\right\}\)
d) \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)
\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=\left(x-1\right)\left(x+3\right)\)
\(x\left(x-2\right)+2\left(x-2\right)=x\left(x+3\right)-1\left(x+3\right)\)
\(x^2-2x+2x-4=x^2+3x-x-3\)
\(\)\(x^2-4=x^2+2x-3\)
\(\Leftrightarrow x^2-x^2-2x+3=4\)
\(-2x+3=4\)
\(-2x=1\)
\(x=-\dfrac{1}{2}\)
bài 1) a) ta có : \(\dfrac{x}{10}=\dfrac{y}{15}\) \(\Leftrightarrow\) \(10y=15x\) \(\Leftrightarrow\) \(10y=15.\dfrac{7}{2}=\dfrac{105}{2}\)
\(\Leftrightarrow y=\dfrac{105}{2}:10=\dfrac{21}{4}\)
vậy \(x+2y-3z=20\Leftrightarrow\) \(\dfrac{7}{2}+2.\dfrac{21}{4}-3z=20\)
\(\Leftrightarrow\) \(-3z=20-14=6\) \(\Leftrightarrow\) \(z=-2\)
vậy \(x=\dfrac{7}{2}\) ; \(y=\dfrac{21}{4}\) ; \(z=-2\)
