I: C/m
a : \(\dfrac{a^2+bc}{b^2+bd}=\dfrac{3a^2+c^2}{3b^2+d^2}\)
b: \(\dfrac{7a+19c}{7b+19d}=\dfrac{a-3c}{b-3d}\)
c : \(\dfrac{a^3+c^3}{b^3+d^3}=\dfrac{4a^3-c^3}{4b^3-d^3}\)
help me
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\left(b+d\ne0\right)\) . Chứng minh: \(\dfrac{4a^2+4c^2}{4b^2+4d^2}=\dfrac{\left(a-c\right)^2}{\left(b-d\right)^2}\)
B1:C/m \(a:\dfrac{a^2+ac}{b^2+bd}=\dfrac{3a^2+c^2}{3b^2+d^2}\)
b: \(\dfrac{7a+19c}{7b+19b}=\dfrac{a-3c}{b-3d}\)
c: \(\dfrac{a^3+c^3}{b^3+a^3}=\dfrac{4a^3-c^3}{4b^3-d^3}\)
help me
cho\(\dfrac{a}{b}=\dfrac{c}{d}\)với c\(\ne\) \(\pm\)1. CMR \(\dfrac{ab}{cd}=\dfrac{\left(a-c\right)^2}{\left(b-d\right)^2}\)
CM phân số
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)
CMR: \(\dfrac{\left(a+b\right)}{\left(a-b\right)}=\dfrac{\left(c+d\right)}{\left(c-d\right)}\)
a, cho \(\dfrac{a}{b}=\dfrac{c}{d}\) (b,d \(\ne\)0) CMR:\(\dfrac{a}{a-b}=\dfrac{c}{c-d}\)
b,cho \(\dfrac{a}{b}=\dfrac{c}{d}\)(b,d \(\ne\)0) CMR:\(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
Câu 1:
a, Chứng minh rằng: Nếu a,b \(\in Z\) và \(a+5b⋮7\) thì \(10a+b⋮7\)
b, Cho a,b,c,d \(\ne0\) và \(b^2=ac;c^2=bd;b^3+c^3+d^3\ne0\)
Chứng minh rằng: \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
c, Cho \(S=\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+\dfrac{24}{25}+...+\dfrac{2499}{2500}\)
Chứng minh rằng: \(S\notin N\)
Câu 2:
a, Cho \(\dfrac{a+b-2017c}{c}=\dfrac{b+c-2017a}{a}=\dfrac{c+a-2017b}{b}\)
Với a,b,c \(\ne0\). Tính P = \(\left(1+\dfrac{a}{b}\right).\left(1+\dfrac{b}{c}\right).\left(1+\dfrac{c}{a}\right)\)
b, Tìm x,y,z biết:
\(\left(x+y\right)^2+4.\left(y-1\right)^2=9\)
Làm được câu nào thì trả lời giúp mình nhé! Ai trả lời mình k cho!
Bài 1: CMR:
a) \(\dfrac{\left(a-b\right)^3}{\left(c-d\right)^3}=\dfrac{3a^3+2b^3}{3c^3+2d^3}\)
b)\(\dfrac{a^{10}+b^{10}}{\left(a+b\right)^{10}}=\dfrac{c^{10}+d^{10}}{\left(c+d\right)^{10}}\)
c)\(\dfrac{a^{2017}}{b^{2017}}=\dfrac{\left(a-c\right)^{2017}}{\left(b-d\right)^{2017}}\)
Bài 2: a) Cho: \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}\) và a,b,c\(\ne\)0;a+b+c\(\ne\)0
So sánh a,b,c
b) Cho \(\dfrac{x}{y}=\dfrac{y}{z}=\dfrac{z}{x}\) và x,y,z\(\ne\)0;x+y+z\(\ne\)0
Tính: \(\dfrac{x^{333}.y^{666}}{z^{999}}\)
c) Cho \(ac=b^2;ab=c^2\left(a+b+c\ne0\right)\)
Tính \(\dfrac{b^{333}}{c^{111}.a^{222}}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) CMR:
a. \(\dfrac{a^2}{b^2}=\dfrac{2c^2-ac}{2d^2-bd}\)
b. \(\dfrac{ma+nb}{ma-nb}=\dfrac{mc+nd}{mc-nd}\)
c. \(\left(\dfrac{a-b}{c-d}\right)^{^{ }3}=\dfrac{a^3+b^3}{c^3+d^3}\) (Làm theo cách Dãy tỉ số bằng nhau)
