Question

1.Cho \(\frac{a}{b}\)= \(\frac{c}{d}\)chứng minh :

a. \(\frac{a+c}{b+d}\)=\(\frac{a-c}{b-d}\)

b. \(\frac{2a+3b}{2a-3b}\)=\(\frac{2c+3d}{3c-3d}\)

2. tìm x, biết :

a. \(\frac{-2,6}{x}\)=\(\frac{-12}{42}\)

b. \(\frac{x^2}{6}\)= \(\frac{24}{25}\)

Answer 1

\(a,\frac{-2,6}{x}=-\frac{12}{42}\)

\(\Leftrightarrow\left(-2,6\right).42=-12x\)

\(\Leftrightarrow-12x=-\frac{546}{5}\)

\(\Leftrightarrow x=\frac{91}{10}\)

Answer 2

\(b,\frac{x^2}{6}=\frac{24}{25}\)

\(\Leftrightarrow25x^2=24.6\)

\(\Leftrightarrow25x^2=144\)

\(\Leftrightarrow x^2=\frac{144}{25}\)

\(\Leftrightarrow x=\frac{12}{5}\)

Answer 3

Bài 1:

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

\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{a-c}{b-d}\)

Vậy \(\frac{a+c}{b+d}=\frac{a-c}{b-d}\)

b) Ta có: \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\Leftrightarrow\frac{2a}{2c}=\frac{3b}{3d}\)

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

\(\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)

Vì \(\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)nên \(\frac{2a+3b}{2a-3b}=\frac{2c+3d}{2c-3d}\left(ĐPCM\right)\)

Bài 2:

\(\text{a)}\frac{-2,6}{x}=\frac{-12}{42}\)

\(\Rightarrow-12.x=-2,6.42\)

\(\Rightarrow-12.x=-109,2\)

\(\Rightarrow x=\frac{-109,2}{-12}=9,1\)

\(\text{b)}\frac{x^2}{6}=\frac{24}{25}\)

\(\Rightarrow x^2.25=6.24\)

\(\Rightarrow x^2.25=144\)

\(\Rightarrow x^2=\frac{144}{25}\)

\(\Rightarrow x=\pm\sqrt{\frac{144}{25}}=\pm\frac{12}{5}\)

Answer 4

(a+c)(b-d)=(a-c)(b+d)
<=>ab+bc-ad-cd=ab-bc+ad-cd
<=>ab+bc-ad-cd-ab+bc-ad+cd=0
<=>2bc=2ad
<=>bc=ad

​<=>a/b=c/d