\(\frac{63+Y}{81+Y}=1-\frac{1}{8}=??\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1, \(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{8}\right):\left(12\frac{1}{9}\right)=0\)
\(\left(\frac{6.9+5}{9}+x-\frac{117}{8}\right):\frac{12.9+1}{9}=\frac{1}{2}\)
( . là nhân nha)
\(\left(\frac{59}{9}-\frac{117}{8}+x\right):\frac{109}{9}=\frac{1}{2}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{1}{2}\cdot\frac{109}{9}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{109}{18}\)
\(x=\frac{109}{18}-\frac{59}{9}+\frac{117}{8}\)
\(x=\frac{113}{8}\)
( \(\left(y+\frac{1}{3}\right)+\left(y+\frac{2}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)
\(y+\frac{1}{3}+y+\frac{2}{9}+y+\frac{1}{27}+y+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{1}{3}+\frac{2}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{49}{81}=\frac{56}{81}\)
\(4y=\frac{7}{81}\)
y = 7/81:4
y = 7/324
Đặt: \(\left\{{}\begin{matrix}\frac{1}{x+y}=a\\\frac{1}{x-y}=b\end{matrix}\right.\)
Hệ đã cho trở thành: \(\left\{{}\begin{matrix}108b+63a=7\\81b+84a=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{1}{27}\\b=\frac{1}{21}\end{matrix}\right.\)
\(\Rightarrow\frac{1}{x+y}=\frac{1}{27}\Rightarrow x+y=27\)
Và: \(\frac{1}{x-y}=\frac{1}{21}\Rightarrow x-y=21\)
Ta có hệ: \(\left\{{}\begin{matrix}x+y=27\\x-y=21\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=24\\y=3\end{matrix}\right.\)
Vậy ................
* ĐK: \(x\ne+-y\)
\(\frac{108}{y+x}+\frac{63}{y-x}=7_{\left(1\right)}\)
\(\frac{81}{y+x}+\frac{84}{y-x}=7_{\left(2\right)}\)
Trừ theo vế với vế (1) cho (2) ta có: \(\frac{27}{y+x}-\frac{21}{y-x}=0\)<=> \(\frac{9}{y+x}=\frac{7}{y-x}\)<=> 9(y-x) = 7(y +x)
<=> y = 8x
Thay y = 8x vào PT (1) => \(\frac{108}{9x}+\frac{63}{7x}=7\)<=> \(\frac{12}{x}+\frac{9}{x}=7\) <=> 21/x = 7 => x = 3 => y =24
Vậy HPT cho có nghiệm (x; y) = (3; 24)
Đặt \(\frac{1}{x}=a;\frac{1}{y}=b;\frac{1}{z}=c\)
\(hpt\Leftrightarrow\left\{{}\begin{matrix}a+b=\frac{1}{72}\\a+c=\frac{1}{63}\\b+c=\frac{1}{56}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a+b=\frac{1}{72}\\a-b=\frac{1}{63}-\frac{1}{56}\\b+c=\frac{1}{56}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{1}{72}-b\\2b=\frac{1}{72}+\frac{1}{504}\\c=\frac{1}{56}-b\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{1}{72}-b\\b=\frac{\frac{1}{72}+\frac{1}{504}}{2}=\frac{1}{126}\\c=\frac{1}{56}-b\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{1}{72}-\frac{1}{126}=\frac{1}{168}\\b=\frac{1}{126}\\c=\frac{1}{56}-\frac{1}{126}=\frac{5}{504}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=168\\y=126\\z=100,8\end{matrix}\right.\)
\(\frac{63+y}{81+y}=1-\frac{1}{8}\)
\(\Rightarrow\frac{63+y}{81+y}=\frac{7}{8}\)
\(\Rightarrow(63+y).8=\left(81+y\right).7\)
\(\Rightarrow504+8y=567+7y\)
\(\Rightarrow567-504=8y-7y\)
\(\Rightarrow y=63\)