cho \(\frac{a}{b}=\frac{c}{d}\left(b,d\ne0;b\ne d,-d\right)\)
Chứng minh \(\left(\frac{a-b}{c-d}\right)^{2018}=\frac{a^{2018}+b^{2018}}{c^{2018}+d^{2018}}\)
Cho \(\frac{a}{b+c+d}=\frac{b}{c+d+a}=\frac{c}{b+d+a}=\frac{d}{a+b+c}\)
Tính \(A=\frac{a^{2018}}{b^{2018}}+\frac{b^{2018}}{c^{2018}}+\frac{c^{2018}}{d^{2018}}+\frac{d^{2018}}{a^{2018}}\)
Cho a, b, c thỏa mãn \(\frac{a}{2017}=\frac{b}{2018}=\frac{c}{2019}\). Chứng minh \(4\left(a-b\right)\left(c-d\right)=\left(c-a\right)^2\)
Cho tỷ lệ thức \(\frac{a}{b}=\frac{c}{d}\)
chứng tỏ :
a,\(\left(\frac{a-b}{c-d}\right)^2=\frac{ab}{c\text{d}}\)
b,\(\frac{2017\text{a}-2018b}{2017c+2018\text{d}}=\frac{2017c-2018\text{d}}{2018\text{a}+2019b}\)
Các bạn giúp mih nha! (mình cần gấp) thnk các bạn nha
â , tính M = \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right).......\left(1+\frac{1}{2017}\right)\left(1+\frac{1}{2018}\right)\)
b , Cho A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2017}-\frac{1}{2018}\)
c , B = \(\frac{1}{1010}+\frac{1}{1011}+.....+\frac{1}{2017}+\frac{1}{2018}.tinh\left(\frac{A}{B}\right)^{2018}\)
1/ Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh \(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+c^2}\)
2/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\) và a + b + c \(\ne\)0. Tính \(M=\frac{a^{49}.b^{51}}{c^{100}}\)
3/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{2018}=\frac{2018}{a}\) và \(a+b+c\ne\left(-2018\right)\). Tính \(Q=a+b-c\)
Cho \(\frac{a}{2016}=\frac{b}{2017}=\frac{c}{2018}.Chứngminh4\left(a-b\right).\left(b.c\right)=\left(c-a\right)^2\)
Cho các số \(a,b,c,d\ne0\). Tính
\(T=x^{2019}+y^{2019}+z^{2019}+t^{2019}\)
Biết \(x,y,z,t\)thoả mãn: \(\frac{x^{2018}+y^{2018}+z^{2018}+t^{2018}}{a^2+b^2+c^2+d^2}=\frac{x^{2018}}{a^2}+\frac{y^{2018}}{b^2}+\frac{z^{2018}}{c^2}+\frac{t^{2018}}{d^2}\)
Cho 4 số a,b,c,d khác 0 thỏa mãn : \(a+c-2b^{2018}+\left|2bd-cd-cb\right|^{2019}=0\)
Chứng minh : \(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)