(+) \(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow ad=bc\)
(+) \(\dfrac{2a+3b}{2a-3b}=\dfrac{2c+3d}{2c-3d}\) (*)
\(\Leftrightarrow4ac+6bc-6ad-9bd=4ac-6bc+6ad-9bd\)
\(\Leftrightarrow12bc=12ad\Leftrightarrow bc=ad\) (đúng)
Vậy (*) đúng (đpcm)
chung minh : neu \(\dfrac{a}{b}=\dfrac{c}{d}\) thi :
a,\(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)
b,\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
Tìm a,b,c biết:
a/\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}\)và a.b.c=810
b/\(\dfrac{a}{4}=\dfrac{b}{3}=\dfrac{c}{9}\)và \(a-3b+4c=62\)
c/\(\dfrac{2a}{3}=\dfrac{3b}{4}=\dfrac{4c}{5}\)và a+b+c=49
d/\(\dfrac{a}{b}=\dfrac{9}{7}\)và\(\dfrac{b}{c}=\dfrac{7}{3}\),a-b+c=15
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) CMR :
\(\dfrac{ab}{cd}=\dfrac{a^2-b^2}{c^2-d^2}\)
Thay tỉ số các số hữu tỉ số giữa các số nguyên:
a/3,7:4,5
b/\(\dfrac{4}{35}:\dfrac{2}{5}\)
c/\(2\dfrac{1}{3}:\dfrac{3}{4}\)
d/\(3\dfrac{1}{7}:1\dfrac{2}{3}\)
e/2:0,005
f/\(2\dfrac{3}{5}:3,7\)
Tìm x:
\(\dfrac{x}{-18}=\dfrac{-50}{x};\\ 1\dfrac{1}{3}:\left(-0,08\right)=\dfrac{2}{3}:\left(-0,1x\right);\\ x=\dfrac{a}{b+c}=\dfrac{b}{c+a}=\dfrac{c}{b+a};\\ \dfrac{x^2}{6}=\dfrac{24}{25};\dfrac{x+1}{x-5}=\dfrac{0,5}{0,6};\\ \dfrac{2}{3}x:\dfrac{1}{5}=1\dfrac{1}{3}:\dfrac{1}{4};\\ 1,35:0,2=1,25:0,1x\)
tim x, y, z biet :
a, \(\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}\) va 2x + 3y - z = 186
b, \(\dfrac{x}{3}=\dfrac{y}{4}\) va \(\dfrac{y}{5}=\dfrac{z}{7}\) va 2x + 3y - z = 327
c, 2x = 3y = 5z va x + y - z = 95
d, \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\) va xyz = 810
CMR:Nếu \(\dfrac{a}{b}\)=\(\dfrac{b}{c}\)=\(\dfrac{c}{a}\)thì a=b=c
a/Tìm GTNN của biểu thức A=\(\left(2x+\dfrac{1}{3}\right)^4-1\)
b/Tìm GTLN của biểu thức B=\(-\left(\dfrac{4}{9}x-\dfrac{2}{15}\right)^{2018}+3\)
1: Tính hợp lí:
a, \(\dfrac{11}{125}\)- \(\dfrac{17}{18}-\dfrac{5}{7}+\dfrac{4}{9}\)+ \(\dfrac{17}{14}\)
b,\(-1\dfrac{5}{7}.15+\dfrac{2}{7}.\left(-15\right)+\left(-105\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\)
2: Tìm x:
a, \(\dfrac{11}{13}-\left(\dfrac{5}{42}-x\right)=-\left(\dfrac{15}{28}-\dfrac{11}{13}\right)\)
b,\(|x+\dfrac{4}{15}|-|-3,75|=-|-2,15|\)
c, \(^{7^{x+2}}+2.7^{x-1}=345\)