1a)tìm x,y biết: \(4+\frac{x}{7+y}=\frac{4}{7}and:x+y=22\)
b)cho \(\frac{x}{3}=\frac{y}{4}\)và \(\frac{y}{5}=\frac{z}{6}\). Tính M=\(\frac{2x+3y+4z}{3x+4y+5z}\)
c) tìm x biết \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}=2^x\)
d)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2x\)
2. Tính:P=\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+..+16\right)\)
Câu b) tạm thời ko bít làm =.=
Bài 1 :
\(d)\) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2x\)
\(\Leftrightarrow\)\(\frac{4^5.4}{3^5.3}.\frac{6^5.6}{2^5.2}=2x\)
\(\Leftrightarrow\)\(\frac{4^6}{3^6}.\frac{6^6}{2^6}=2x\)
\(\Leftrightarrow\)\(\frac{2^{12}}{3^6}.\frac{2^6.3^6}{2^6}=2x\)
\(\Leftrightarrow\)\(\frac{2^{12}}{3^6}.\frac{3^6}{1}=2x\)
\(\Leftrightarrow\)\(2^{12}=2x\)
\(\Leftrightarrow\)\(x=\frac{2^{12}}{2}\)
\(\Leftrightarrow\)\(x=2^{11}\)
\(\Leftrightarrow\)\(x=2048\)
Vậy \(x=2048\)
Chúc bạn học tốt ~
Bài 1 :
\(a)\) Ta có :
\(4+\frac{x}{7+y}=\frac{4}{7}\)
\(\Leftrightarrow\)\(\frac{x}{7+y}=\frac{4}{7}-4\)
\(\Leftrightarrow\)\(\frac{x}{7+y}=\frac{-24}{7}\)
\(\Leftrightarrow\)\(\frac{x}{-24}=\frac{7+y}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{-24}=\frac{7+y}{7}=\frac{x+7+y}{-24+7}=\frac{22+7}{-17}=\frac{29}{-17}=\frac{-29}{17}\)
Do đó :
\(\frac{x}{-24}=\frac{-29}{17}\)\(\Rightarrow\)\(x=\frac{-29}{17}.\left(-24\right)=\frac{696}{17}\)
\(\frac{7+y}{7}=\frac{-29}{17}\)\(\Rightarrow\)\(y=\frac{-29}{17}.7-7=\frac{-322}{17}\)
Vậy \(x=\frac{696}{17}\) và \(y=\frac{-322}{17}\)
Chúc bạn học tốt ~
2.
Ta có 1+2+...+n=n.(n+1):2
=>P=\(1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+...+\)\(\frac{1}{16}.\frac{16.17}{2}\)=1+\(\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}\)=1+\(\frac{1}{2}.\left(3=4+..=17\right)\)
=1+\(\frac{1}{2}.153=1+\frac{153}{2}=\frac{155}{2}\)
a) Có: \(4+\frac{x}{7+y}=\frac{4}{7}\)
\(\Rightarrow\frac{x}{7+y}=-\frac{24}{7}\)
\(\Rightarrow7x=-168-24y\)
\(\Rightarrow7x+24y=-168\)
\(\Rightarrow7\left(x+y\right)+17y=-168\)
\(\Rightarrow154+17y=-168\)
\(\Rightarrow y=-\frac{322}{17}\)
\(\Rightarrow x=\frac{696}{17}\)
Có: \(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{5}=\frac{z}{6}\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{3y}{4}\\z=\frac{6y}{5}\end{cases}}}\left(1\right)\)
Thay (1) vào M, ta đc: \(M=\frac{2.\frac{3y}{4}+3y+4.\frac{6y}{5}}{3.\frac{3y}{4}+4y+5.\frac{6y}{5}}\)
\(=\frac{\frac{3}{2}y+3y+\frac{24}{5}y}{\frac{9}{4}y+4y+6y}\)
\(=\frac{\frac{93}{10}y}{\frac{49}{4}y}=\frac{93}{10}:\frac{49}{4}=\frac{186}{245}\)
Vậy \(M=\frac{186}{245}\)
c) Có: \(\frac{1}{4}.\frac{2}{6}...\frac{30}{62}.\frac{31}{64}=2^x\)
\(\frac{1.2...30.31}{4.6...62.64}=2^x\)
\(\frac{\left(2.3...30.31\right)}{2\left(2.3...31\right).64}=2^x\)
\(\frac{1}{2.64}=2^x\)
\(2^x=\frac{1}{2^7}=2^{-7}\)
\(\Rightarrow x=-7\)
d)Có: \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2x\)
\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2x\)
\(\Rightarrow\frac{4^6}{3^6}.\frac{6^6}{2^6}=2x\)
\(\Rightarrow\frac{\left(2.2\right)^6.\left(2.3\right)^6}{3^6.2^6}=2x\)
\(\Rightarrow\frac{2^6.2^6.2^6.3^6}{3^6.2^6}=2x\)
\(\Rightarrow2^{12}=2x\)
\(\Rightarrow x=2^{11}=2048\)
