\(\dfrac{x_1}{a_1}=\dfrac{x_2}{a_2}=...=\dfrac{x_n}{a_n}=\dfrac{x_1+x_2+...+x_{n-1}+x_n}{a_1+a_2+...+a_{n-1}+a_n}\)
\(=\dfrac{c}{a_1+a_2+...+a_n}\)
Suy ra:
\(x_1=\dfrac{a_1.c}{a_1+a_2+...+a_n}\)
\(x_2=\dfrac{a_2.c}{a_1+a_2+...+a_n}\)
.........................................
\(x_n=\dfrac{a_n.c}{a_1+a_2+...+a_n}\)
Cho \(a_1;a_2;a_3;a_4\ne0\). Biết \(a^2_2=a_1.a_3;a^2_3=a_2.a_4\)và \(a^3_2+8a^3_3+125a_4^3\ne0\)
CMR: \(\dfrac{a_1}{a_4}=\dfrac{a_1^3+8a^3_2+125a_3^3}{a^3_2+8a_3^3+125a^3_4}\)
Cho đa thức \(P\left(x\right)=ax^2+bx+c\). Trong đó \(a,b,c\) là các hằng số thỏa mãn \(\dfrac{a}{1}=\dfrac{b}{2}=\dfrac{c}{3}\) và \(a\ne0\). Tính \(\dfrac{P\left(-2\right)-3P\left(1\right)}{a}\).
tính A= \(\left(1-\dfrac{1}{2}\right)\)\(\left(1-\dfrac{1}{3}\right)\)\(\left(1-\dfrac{1}{4}\right)\).....\(\left(1-\dfrac{1}{n+1}\right)\)
( n là số tự nhiên )
1.Cho \(\dfrac{m-n}{p-q}\)=\(\dfrac{n}{q}\). Chứng minh\(\dfrac{m^2+n^2}{p^2+q^2}=\dfrac{\left(m+n\right)^2}{\left(p+q\right)^2}\)(Giả thiết các tỉ số đều có nghĩa)
2.Cho \(\dfrac{2}{a}=\dfrac{1}{b}+\dfrac{1}{c}\)(a,b,c\(\ne\)0,a\(\ne\)c). Chứng minh rằng:\(\dfrac{b}{c}=\dfrac{b-a}{a-c}\)
3.Cho b2=ac.Chứng minh:\(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)
4.Cho \(\dfrac{x}{3}\)=\(\dfrac{y}{4}\) và \(\dfrac{y}{5}=\dfrac{z}{6}\). Tính \(M=\dfrac{2x+3y+4z}{3x+4y+5z}\)
Các bạn ơi giúp mình vs T-T
1) A = \(\dfrac{15}{24}+\dfrac{7}{21}+\dfrac{9}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)
2) B = \(16\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)-28\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)\)
3) C = \(25.\left(-\dfrac{1}{3}\right)^3+\dfrac{1}{5}-2.\left(-\dfrac{1}{2}\right)^2-\dfrac{1}{2}\)
4) D = \(\left(-2\right)^3.\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)
5) E = \(5\sqrt{6}-4\sqrt{9}+\sqrt{25}-0,3\sqrt{400}\)
a) \(\dfrac{11}{13}-\left(\dfrac{5}{42}-x\right)=\left(\dfrac{15}{28}-\dfrac{11}{13}\right)\)
b) \(\left(\dfrac{7}{2}-2x\right)x3\dfrac{2}{5}+1\dfrac{4}{5}=7\dfrac{6}{5}\)
c) \(\left|2x-\dfrac{1}{3}\right|=\dfrac{5}{3}-2\)
d) (2x-1)3= -27
e) \(\dfrac{16}{2x}=1\)
tìm x, biết:
a.\(\dfrac{5}{12}\sqrt{x}-\dfrac{1}{6}=\dfrac{1}{3}\)
b. \(\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\left|\dfrac{-3}{4}\right|\)
giúp mk nhanh nha đan cần gấp
a)\(\dfrac{x+1}{2}\)=\(\dfrac{2x+3}{5}\)
b)\(\left|x-1\right|\) + 3\(\left|y+1\right|\) + \(\left|z+2\right|=0\)
c)\(\dfrac{x-2}{4}=\dfrac{5-3x}{4}\)
d)\(\dfrac{x+2}{4}=\dfrac{4}{x+2}\)
e)\(\dfrac{x-1}{5}=\dfrac{-20}{x-1}\)
Tìm n:
a) \(\left(\dfrac{1}{2}\right)^n=\dfrac{1}{32}\)
b) \(\left(\dfrac{343}{125}\right)=\left(\dfrac{7}{5}\right)^n\)
c) \(\dfrac{16}{2^n}=2\)
d) \(\dfrac{\left(-3\right)^n}{81}=-27\)
e) 8n : 2n =4
f) 32 . 3n = 35
g) ( 22 : 4 ).2n = 4
h) 3-2 . 34 . 3n = 37