\(\frac{^{x1}}{x2}\)=\(\frac{x3}{x2}\)=\(\frac{x3}{x4}\)=....................................=\(\frac{x2017}{x2018}\)
va \(\frac{a1}{a2018}\)= \(^{5^{ }2017}\)
biet \(x2+x3+x4+......................+x2018\ne0\)
tinh S=\(\frac{x1+x2+x3+.....................+x2017}{x2+x3+x4+.....................+x2018}\)
CHO \(\frac{x1}{x2}=\frac{x3}{x4};x1+x4\)khác 0
chứng minh rằng \(\frac{2017\cdot\left(x1\right)^2+\left(x3\right)^2}{2017\cdot\left(x2\right)^2+\left(x4\right)^2}=\frac{\left(x1+x3\right)^2}{\left(x2+x4\right)^2}\)
Tìm X1 ,x2 ,x3,x4,x5
\(\frac{x1-1}{5}=\frac{x2-2}{4}=\frac{x3-3}{3}=\frac{x4-4}{2}=\frac{x5-5}{1}\)\(v\text{à}\)X1 +x2+x3+x4+x5 =30
\(\frac{x1}{x2}=\frac{x2}{x3}=\frac{x3}{x4}=......=\frac{x2008}{x2009}\)
CMR : \(\left(\frac{x1+x2+x3+....+x2008}{x2+x3+x4+...+x2009}\right)=\frac{x1}{x2009}\) xin haay giai ra gium minh
Câu 1: Cho tỉ lệ thức: \(\frac{a}{b}=\frac{c}{d}\)CMR:
a)\(\frac{a^n+b^n}{c^n+d^n}=\frac{a^n-b^n}{c^n-d^n}\) b) \(\left(\frac{a+b}{c+d}\right)^2=\frac{a^2+b^2}{c^2+d^2}\)
Câu 2: CMR: nếu \(\frac{a1}{a2}=\frac{a2}{a3}=\frac{a3}{a4}=...=\frac{a2017}{2018}\)thì \(\frac{a1}{a2018}=\left(\frac{a1+a2+a3+...+a2017}{a2+a3+a4+...+a2018}\right)^{2017}\)
Câu 3: Cho 6 số: x1, x2, x3, x4, x5, x6 khác 0 thỏa mãn: \(x2^2=x1.x3\); \(x3^2=x2.x4\); \(x4^2=x4.x5\); \(x5^2=x5.x6\)
CTR: \(\frac{x1}{x6}=\left(\frac{x1+x2+...+x5}{x2+x3+...+x6}\right)^5\)
cho x1x2=x2x3=x3x4...=x2016x2017x1x2=x2x3=x3x4...=x2016x2017
chứng minh: (x1+x2+x3+...+x2016x2+x3+x4+...+x2017)2016=x1x2017(x1+x2+x3+...+x2016x2+x3+x4+...+x2017)2016=x1x2017
Cho (x2)^2=x1.x3;(x3)^2=x2.x4.Chứng minh rằng: (x1+x2+x3)^2/(x2+x3+x4)^2=x1^2+x2^2+x3^3/x2^2+x3^3+x4^4
Cho bốn số x1, x2, x3, x4 khác 0 thỏa mãn x22 = x1.x3 ; x23 = x2.x4 Chứng minh rằng: x1/ x4 = (x1 x2 x3 / x2 x3 x4 ) ^3
Cho x1−12017=x2−22016=x3−32016=...=x2017−20171x1−12017=x2−22016=x3−32016=...=x2017−20171 và x1+x2+...+x2017=2017.2018
Tìm x1,x2,...,x2017?
Cho x1−12017=x2−22016=x3−32016=...=x2017−20171x1−12017=x2−22016=x3−32016=...=x2017−20171 và x1+x2+...+x2017=2017.2018
Tìm x1,x2,...,x2017?
