Tìm x, biết: \(\frac{x+11}{39}\)+ \(\frac{x+13}{37}\)+\(\frac{x+15}{35}\)= \(\frac{x+17}{33}\)+\(\frac{x+19}{31}\)+\(\frac{x+31}{29}\)
Giải phương trình \(\frac{x+19}{27}-\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
Bài làm
\(\frac{x+19}{27}-\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
\(\Leftrightarrow\left(\frac{x+19}{27}+1\right)-\left(\frac{x+17}{29}+1\right)=\left(\frac{x+15}{31}+1\right)-\left(\frac{x+13}{33}+1\right)\)
\(\Leftrightarrow\frac{x+46}{27}-\frac{x+46}{29}=\frac{x+46}{31}-\frac{x+46}{33}\)
\(\Leftrightarrow\left(x+46\right).\frac{1}{27}-\left(x+46\right).\frac{1}{29}=\left(x+46\right).\frac{1}{31}-\left(x+46\right).\frac{1}{33}\)
\(\Leftrightarrow\left(x+46\right).\frac{1}{27}-\left(x+46\right).\frac{1}{29}-\left(x+46\right).\frac{1}{31}+\left(x+46\right).\frac{1}{33}=0\)
\(\Leftrightarrow\left(x+46\right)\left(\frac{1}{27}-\frac{1}{29}-\frac{1}{31}\right)=0\)
Mà \(\left(\frac{1}{27}-\frac{1}{29}-\frac{1}{31}\right)>0\forall x\)
\(\Leftrightarrow x+46=0\)
\(\Leftrightarrow x=-46\)
Vậy phương trình trên có tập nghiệm S = { -46 }
# Học tốt #
Tìm x :
\(\frac{x+29}{31}+\frac{x+27}{33}=\frac{x+17}{43}+\frac{x+15}{45}\)
\(\frac{x+29}{31}+\frac{x+27}{33}=\frac{x+17}{43}+\frac{x+15}{45}\)
\(\frac{x+29}{31}+1+\frac{x+27}{33}+1=\frac{x+17}{43}+1+\frac{x+15}{45}+1\)
\(\frac{x+60}{31}+\frac{x+60}{33}=\frac{x+60}{43}+\frac{x+60}{45}\)
\(\left(x+60\right)\left(\frac{1}{31}+\frac{1}{33}-\frac{1}{43}-\frac{1}{45}\right)=0\)
VÌ \(\frac{1}{31}+\frac{1}{33}-\frac{1}{43}-\frac{1}{45}\ne0\)
\(\Rightarrow x+60=0\)
\(\Rightarrow x=-60\)
Câu hỏi của honoka sonoka - Toán lớp 6 - Học toán với OnlineMath
Tìm x, biết:
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)
\(\frac{x+29}{31}-\frac{x +17}{33}=\frac{x+17}{43}-\frac{x+15}{45}\)
Tìm X:
\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(X-\left(\frac{31}{5}+\frac{31}{3\cdot5}+\frac{31}{5\cdot7}+\frac{31}{7\cdot9}+\frac{31}{9\cdot11}+\frac{31}{11\cdot13}\right)=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\frac{10}{39}+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\frac{1984}{195}=\frac{9}{13}\)
\(\Rightarrow X=\frac{9}{13}+\frac{1984}{195}=\frac{163}{15}\)
Tìm x :
x - \(\left(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}=\frac{31}{1.3}+\frac{31}{3.5}+\frac{31}{5.7}+\frac{31}{7.9}+\frac{31}{9.11}+\frac{31}{11.13}\\ \)
\(=\frac{31}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{31}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{31}{2}.\left(1-\frac{1}{13}\right)=\frac{31}{2}.\frac{12}{13}=\frac{31.6}{13}=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\Leftrightarrow x=\frac{195}{13}=15\)
\(x-\left(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\)\(\frac{9}{13}\)(1)
Đặt \(A=\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\)
\(A=31\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(\Rightarrow2A=31\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(2A=31\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(2A=31\left(2-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(2A=31\left(2-\frac{1}{13}\right)\)
\(2A=31.\frac{25}{13}\)
\(2A=\frac{775}{13}\)
\(\Rightarrow A=\frac{775}{13}:2\)
\(A=\frac{775}{26}\)
Thay vào (1) ta có:
\(x-\frac{775}{26}=\frac{9}{13}\)
\(\Leftrightarrow x=\frac{9}{13}+\frac{775}{26}\)
\(\Leftrightarrow x=\frac{61}{2}\)
ai tích mình ,mình tích lại (ai trên 11 điểm tích mới tích lại)
Giải
Hiệu số tuổi bố và con không bao giờ thay đổi.
Hiện nay tuổi con bằng 1/6 tuổi bố. Vậy tuổi bố bằng:
6/6-1 = 6/5 (hiệu )
Sau 4 năm thì tuổi bố bằng:
4/4-1 = 4/3 ( hiệu )
4 năm thì bằng:
4/3 – 6/5 = 2/15 ( hiệu )
Hiệu của tuổi hai bố con là:
4 : 2/15 = 30 ( tuổi )
Tuổi con hiện nay là:
30 : ( 6 - 1 ) = 6 ( tuổi )
Tuổi bố hiện nay là:
6 x 6 = 36 ( tuổi )
Đáp số:
Con: 6 tuổi
Bố: 36 tuổi
\(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}\frac{x+7}{29}\)
\(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)
đề chính xác là như này đúng k cậu=)đề k rõ ràng k aii giúp đc nhé!
\(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)
\(\Leftrightarrow\left(\frac{x+1}{35}+1\right)+\left(\frac{x+3}{33}+1\right)=\left(\frac{x+5}{31}+1\right)+\left(\frac{x+7}{29}+1\right)\)
\(\Leftrightarrow\left(\frac{x+1+35}{35}\right)+\left(\frac{x+3+33}{33}\right)=\left(\frac{x+5+31}{31}\right)+\left(\frac{x+7+29}{29}\right)\)
\(\Leftrightarrow\frac{x+36}{35}+\frac{x+36}{33}=\frac{x+36}{31}+\frac{x+36}{29}\)
\(\Leftrightarrow\frac{x+36}{35}+\frac{x+36}{33}-\frac{x+36}{31}-\frac{x+36}{29}=0\)
\(\Leftrightarrow\left(x+36\right).\left(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\right)=0\)
Vì \(\frac{1}{35}+\frac{1}{33}-\frac{1}{31}-\frac{1}{29}\ne0.\)
\(\Leftrightarrow x+36=0\)
\(\Leftrightarrow x=0-36\)
\(\Leftrightarrow x=-36.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{-36\right\}.\)
Chúc bạn học tốt!
Giải phương trình sau;
a) \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\)
b) \(\left(x-1\right)^3+\left(x+1\right)^3=8\left(x-1\right)^3\)
c) \(\frac{x+19}{27}+\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
Giải các phương trình sau:
a) \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\)
b) \(\left(x-1\right)^3+\left(x+1\right)^3=8\left(x-1\right)^3\)
c)\(\frac{x+19}{27}+\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
Tìm x, biết:
a) \(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)
b) \(\frac{x-10}{1994}+\frac{x-8}{1996}+\frac{x-6}{1998}+\frac{x-4}{2000}+\frac{x-2}{2002}=\frac{x-2002}{2}+\frac{x-2000}{4}+\frac{x-1998}{6}+\frac{x-1996}{8}+\frac{x-1994}{10}\)
a/ (X+1)/35+1+(x+3)/33+1 =(x+5)/31+(x+7)/29+1+1
=>(x+36)/35+(x+36)/33-(x+36)/31-(x+36)/27=0
=>(X+36)(1/35+1/33-1/31-1/29)=0
=> x+36=0(vì c=vế 2 luôn luôn khác 0)
=>x=-36
b/ CMTT câu a
trừ tung phân số cho 1 ta được x=2004