y - 15/8 = 1/2
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Áp dụng BĐT phụ \(a^2+b^2\ge\dfrac{1}{2}\left(a+b\right)^2\Leftrightarrow\left(a-b\right)^2\ge0\)
\(A\ge\dfrac{1}{2}\left(x+y+\dfrac{1}{x}+\dfrac{1}{y}\right)^2\ge\dfrac{1}{2}\left(x+y+\dfrac{4}{x+y}\right)^2=\dfrac{1}{2}\left(1+\dfrac{4}{1}\right)^2=\dfrac{25}{2}\)
Dấu "=" \(x=y=\dfrac{1}{2}\)
Bài 1:
a) \(=\dfrac{8}{15}\left(\dfrac{7}{13}+\dfrac{6}{13}\right)=\dfrac{8}{15}.1=\dfrac{8}{15}\)
b) \(=\dfrac{3.3-7-2.4}{12}=-\dfrac{6}{12}=-\dfrac{1}{2}\)
Bài 2:
\(\dfrac{x}{2,7}=-\dfrac{2}{3,6}\Rightarrow x=\dfrac{\left(-2\right).2,7}{3,6}\Rightarrow x=-\dfrac{3}{2}\)
Bài 3:
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{x+y}{2+5}=-\dfrac{21}{7}=-3\)
\(\Rightarrow\left\{{}\begin{matrix}x=\left(-3\right).2=-6\\y=\left(-3\right).5=-10\end{matrix}\right.\)
\(\frac{1}{5}+\frac{8}{15:y}=\frac{1}{2}\)
\(\frac{8}{15}:y=\frac{1}{2}-\frac{1}{5}\)
\(\frac{8}{15}:y=\frac{3}{10}\)
\(y=\frac{8}{15}:\frac{3}{10}\)
\(y=\frac{16}{9}\)
Vậy suy ra y bằng \(\frac{16}{9}\)
\(\frac{1}{5}+\frac{8}{15}:y=\frac{1}{2}\)
\(\frac{8}{15}:y=\frac{1}{2}-\frac{1}{5}\)
\(y=\frac{8}{15}:\frac{3}{10}\)
\(y=\frac{8.10}{15.3}\)
\(y=\frac{16}{9}\)
Chúc em học tốt^^
\(\dfrac{8}{9}\) : ( 2 - 3 \(\times\) y) = \(\dfrac{5}{3}\)
2 - 3 \(\times\) y = \(\dfrac{8}{9}\) : \(\dfrac{5}{3}\)
2 - 3 \(\times\) y = \(\dfrac{8}{15}\)
3 \(\times\) y = 2 - \(\dfrac{8}{15}\)
3 \(\times\) y = \(\dfrac{22}{15}\)
y = \(\dfrac{22}{15}\) : 3
y = \(\dfrac{22}{45}\)
\(\frac{1,3}{4}\times8-y=1\frac{2}{5}\)
\(\frac{13}{40}\times8-y=\frac{7}{5}\)
\(\frac{13}{5}-y=\frac{7}{5}\)
\(y=\frac{13}{5}-\frac{7}{5}\)
\(y=\frac{6}{5}\)
b) \(\frac{2,3}{4}\div\frac{2}{4}+y=\frac{19}{15}\)
\(\frac{23}{40}\times2+y=\frac{19}{15}\)
\(\frac{23}{20}+y=\frac{19}{15}\)
\(y=\frac{19}{15}-\frac{23}{20}\)
\(y=\frac{7}{60}\)
(2x-1)x(3-y)=15
x là STN => 2x-1 là số lẻ
3-y =>y< hoặc= 3
Ta có : 15x1=15 ;5x3=15
TH1 : 2x-1=15 =>x=8
3-y=1 =>y=2
TH2 : 2x-1=5 => x=3
3-y= 3 => y=0
CÂU 2 BÓ TAY !!! XIN LỖI MIK K BT CÂU ĐÓ
Bài 1 :
a ) Ta có :
\(\left(x+y\right)^2=x^2+y^2+2xy=20+16=36\)
b ) Ta có :
\(x^2+y^2=\left(x+y\right)^2-2xy=64-30=34\)
y=1/2+15/8
y=19/8