\(\Leftrightarrow\dfrac{ab+1}{3}=\dfrac{ac+2}{5}=\dfrac{bc+3}{9}=\dfrac{ab+ac+bc+1+2+3}{3+5+9}=\dfrac{17}{17}=1\)
=>ab+1=3; ac+2=5; bc+3=9
=>ab=2; ac=3; bc=6
=>(abc)^2=2*3*6=36
=>abc=6 hoặc abc=-6
TH1: abc=6
=>c=3; b=2; a=1
TH2: abc=-6
=>c=-3; b=-2; a=1
Cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) chứng minh rằng:
a) \(\dfrac{a}{a-b}\)=\(\dfrac{c}{c-d}\)
b) \(\dfrac{a}{b}\)=\(\dfrac{a+c}{b+d}\)
c)\(\dfrac{a}{3a+b}\)=\(\dfrac{c}{3c+b}\)
d) \(\dfrac{a.c}{b.c}\)=\(\dfrac{a^2+c^2}{b^2+d^2}\)
e) \(\dfrac{a.b}{c.d}\)=\(\dfrac{a^2-b^2}{c^2-d^2}\)
f) \(\dfrac{a.b}{c.d}\)=\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
Cho các số a,b,c,d ≠ 0 và \(b^2=a.c\) ; \(c^2=b.d\) ; \(b^3+c^3+d^3\ne0\). C/m rằng :\(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
cho \(\dfrac{a}{b}\) =\(\dfrac{c}{d}\) cm rằng
a) \(\dfrac{a}{a-b}\) =\(\dfrac{c}{c-d}\) b)\(\dfrac{a}{b}\) =\(\dfrac{a+c}{b+d}\) c) \(\dfrac{a}{3a+d}\) =\(\dfrac{c}{3c+d}\) d)\(\dfrac{a.c}{b.d}\) =\(\dfrac{a^2+c^2}{b^2+c^2}\) e)\(\dfrac{a.b}{c.d}\) =\(\dfrac{a^2-b^2}{c^2-d^2}\) f)\(\dfrac{a.b}{c.d}\) =\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
mn giúp mk vs ạ! thanks
Cho đẳng thức a.b = 3.6. Tỉ lệ thức nào sau đây sai:
A. \(\dfrac{a}{b}=\dfrac{3}{6}\). B. \(\dfrac{a}{3}=\dfrac{6}{b}\) C. \(\dfrac{a}{6}=\dfrac{3}{b}\)
cho a, b, c khác 0 và \(^{a^2}\)=b.c
chứng minh \(\dfrac{a^2+c^2}{b^2+a^2}=\dfrac{c}{b}\)
Cho \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{a.b}{c.d}\) với a;b;c;d khác 0 và c khác +- d
CMR: \(\dfrac{a}{b}=\dfrac{c}{d} \) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)
Tìm x, biết :
\(a.3\dfrac{4}{5}:40\dfrac{8}{15}=0,25:x\)
\(b.\left(x+1\right):\dfrac{5}{6}=20:3\)
\(c.\dfrac{7}{x-1}=\dfrac{x+1}{9}\)
Bài 1: Rút gọn
B= \(\dfrac{1}{2}\)+ (\(\dfrac{1}{2}\))\(^2\)+ (\(\dfrac{1}{2}\))\(^3\)+ (\(\dfrac{1}{2}\))\(^4\)+............+ (\(\dfrac{1}{2}\))\(^{98}\)+ (\(\dfrac{1}{2}\))\(^{99}\)
Bài 2: Tính
a) \(\dfrac{45^{10}.2^{10}}{75^{15}}\)
b) \(\dfrac{2^{15}.9^4}{6^3.8^3}\)
c)\(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}\)
d) \(\dfrac{81^{11}.3^{17}}{27^{10}.9^{15}}\)
Bài 3: Tìm x, biết
a) (2\(x\) + 4)\(^2\) = \(\dfrac{1}{4}\)
b) (2\(x\) - 3)\(^2\) = 36
c) 5\(^{x+2}\) = 625
d) (\(x\) - 1) \(^{x+2}\) = (\(x\) - 1)\(^{x+4}\)
Cho tỉ lệ thức \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) Chứng minh:
1)\(\dfrac{a-b}{b}\)=\(\dfrac{c-d}{d}\) 2)\(\dfrac{a-b}{a}\)=\(\dfrac{c-d}{c}\)
giải giúp mk vss
