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Bài 1a:
\(\frac{4,6}{1,4}\) = \(\frac{11,5}{5x}\)
4,6 x 5\(x\) = 11,5 x 1,4
23\(x\) = 16,1
\(x\) = 16,1 : 23
\(x\) = 0,7
Vậy \(x\) = 0,7
Bài 1b:
\(\frac{x^2}{6}\) = \(\frac{24}{25}\)
25\(x^2\) = 24.6
25\(x^2\) = 144
\(x^2\) = 144/25
\(x\) = - 12/5 hoặc \(x\) = 12/5
Vậy \(x\) ∈ {-12/5; 12/5}
Bài 1c:
\(\frac{x+2}{2}\) = \(\frac{1}{1-x}\)
(\(x\) + 2)(1 - \(x\)) = 1.2
\(x\) - \(x^2\) + 2 - 2\(x\) = 2
\(x^2\) + (2\(x\) - \(x\)) + 2 - 2 = 0
\(x^2\) + \(x\) + 0 = 0
\(x\)(\(x\) + 1) = 0
\(x\) = 0
\(x\) + 1 = 0
\(x\) = - 1
Vậy \(x\) ∈ {-1; 0}
Bài 2:
a) \(\frac{x}{-27}=\frac{-3}{x}\Leftrightarrow-\frac{x}{27}=-\frac{3}{x}\Leftrightarrow-x.x=\left(-27\right).\left(-3\right)\Leftrightarrow-x^2=-81\Leftrightarrow\orbr{\begin{cases}x=9\\x=-9\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=9\\x=-9\end{cases}}\)
b) \(\frac{-9}{x}=\frac{-x}{\frac{4}{49}}\Leftrightarrow-\frac{9}{x}=-\frac{49x}{4}\Leftrightarrow-9.4=-x.49x\Leftrightarrow-36=-49x^2\Leftrightarrow\orbr{\begin{cases}x=\frac{6}{7}\\x=-\frac{6}{7}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{6}{7}\\x=-\frac{6}{7}\end{cases}}\)
Bài 3:
a) \(\frac{x}{1,2}=\frac{5}{6}\)
⇒ \(x.6=5.1,2\)
⇒ \(x.6=6\)
⇒ \(x=6:6\)
⇒ \(x=1\)
Vậy \(x=1.\)
b) \(\frac{5}{9}:x=\frac{7}{4}:\frac{3}{10}\)
⇒ \(\frac{5}{9}:x=\frac{35}{6}\)
⇒ \(x=\frac{5}{9}:\frac{35}{6}\)
⇒ \(x=\frac{2}{21}\)
Vậy \(x=\frac{2}{21}.\)
Bài 5:
Ta có: \(\frac{a+b}{c+d}=\frac{b+c}{d+a}\)
\(\Rightarrow\left(a+b\right).\left(d+a\right)=\left(b+c\right).\left(c+d\right)\)
\(\Rightarrow ad+a^2+bd+ba=bc+bd+c^2+cd\)
\(\Rightarrow a^2+a.\left(b+d\right)=c^2+c.\left(b+d\right)\)
\(\Rightarrow a.\left(b+d\right)=c.\left(b+d\right)\)
\(\Rightarrow a=c\left(đpcm\right).\)
Chúc bạn học tốt!
\(1.\)
\(a,\)
\(7.\left(-28\right)=\left(-49\right).4\)
Ta có : \(\frac{7}{-49}=\frac{4}{-28}\) \(\frac{-28}{4}=\frac{-49}{7}\)
\(\frac{7}{4}=\frac{-49}{-28}\) \(\frac{-28}{-49}=\frac{4}{7}\)
\(b,\)
\(0,36.4,25=0,9.1,7\)
Ta có : \(\frac{0,36}{0,9}=\frac{1,7}{4,25}\) \(\frac{0,36}{1,7}=\frac{0,9}{4,25}\)
\(\frac{4,25}{0,9}=\frac{1,7}{0,36}\) \(\frac{4,25}{1,7}=\frac{0,9}{0,36}\)
Bài 2:
a: =>x/4=1/8
hay x=1/2
b: \(\Leftrightarrow\dfrac{x}{-5}=\dfrac{11}{6}\)
hay x=-55/6
c: \(\Leftrightarrow\dfrac{-3.5}{x}=\dfrac{4.25}{8}\)
hay x=-112/17