Tìm y
\(y+1\frac{21}{22}=2\frac{43}{44}\)
Tìm y biết: \(\frac{y}{1+2}+\frac{y}{1+2+3}+....+\frac{y}{1+2+3+...+43+44}=\frac{27}{44}\)
1) có thể tìm đc 2 số nguyên x,y sao cho 45x+10y=-20152016 ko?
2)CMR:A=\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+\frac{1}{44}+\frac{1}{45}+...+\frac{1}{80}>\frac{7}{12}\)
gọi 1/41+1/42+1/43+...+1/79+1/80 là A
ta có:1/41>1/60,1/42>1/60,1/43>1/60,...,1/60=1/60
=>1/41+1/42+1/43+...+1/60>1/60
1/61>1/80,..................................,1/80=1/80
=>1/61+1/62+............+1/80>1/80
=>1/41+1/42+1/43+...+1/79+1/80>1/60+1/80
lại có 7/12=1/4+1/3
1/60.20=1/3 và 1/80.20=1/4
=>1/41+1/42+1/43+...+1/79+1/80>1/3+1/4
=>1/41+1/42+1/43+...+1/79+1/80>7/12
Tìm các cặp số tự nhiên (x,y) thỏa mãn x2\(\left(\frac{1}{y}-\frac{1}{43}\right)\)+y2\(\left(\frac{1}{x}-\frac{1}{43}\right)\)+x+y=0
đkxđ: \(x,y\ne0\)
Khai triển ra ta được\(\frac{x^2}{y}-\frac{x^2}{43}+\frac{y^2}{x}-\frac{y^2}{43}+x+y=0\)
<=> \(\frac{x^2+y^2}{y}+\frac{x^2+y^2}{x}-\frac{x^2+y^2}{43}=0\)
<=>\(\frac{1}{x}+\frac{1}{y}-\frac{1}{43}=0\)
<=> \(\frac{x+y}{xy}=\frac{1}{43}\)
<=>\(43\left(x+y\right)-xy=0\)\(\orbr{\begin{cases}\hept{\begin{cases}43-x=1849\\43-y=1\end{cases}}\\\hept{\begin{cases}43-x=1\\43-y=1849\end{cases}}\end{cases}}\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}x=42\\y=-1806\end{cases}}\\\hept{\begin{cases}x=-1806\\y=42\end{cases}}\end{cases}}\)
<=>\(\left(43-x\right)\left(43-y\right)=1849\)(tự phân tích nhân tử)
Tự giải phương trình ước số ra nghiệm (x,y)={(42;-1806);(-1806:42)}
Tìm các cặp số tự nhiên (x,y) thoả mãn x2 (\(\frac{1}{y}-\frac{1}{43}\)) +y2 (\(\frac{1}{x}-\frac{1}{43}\)) +x+y=0
1 tim x,y,z biet
\(\frac{-4}{x}=\frac{y}{-14}=\frac{12}{21}=\frac{z}{-63}\)
2 tim n thuoc z n khac 0
a \(\frac{1111100:n}{23331:n}+\frac{-10}{-21}\)
b \(\frac{1075:n}{600:n}=\frac{43}{24}\)
So Sánh
a,\(7.2^{13}\upsilonà2^{16}\)
b, \(21^{15}và27^5.49^8\)
c,\(72^{45}-72^{44}và72^{^{ }44}72^{43}\)
d, \(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right)...\left(\frac{1}{100^2}-1\right)và-\frac{1}{2}\)
a, 7.213 và 216
ta có: 216 = 213. 23 = 213 .8
vì 7. 213 < 213 .8 nên 7.213 <216
\(\left(\frac{22}{43}+\frac{1234}{5678}-\frac{17}{83}\right)-\left(\frac{66}{83}-\frac{21}{43}\right)\)giúp mik vs thak nhìu
Chứng minh rằng:\(\frac{43}{44}\le\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}+2015\sqrt{2016}}\le\frac{44}{45}\)
Tìm y,biết:
a,\(y-\frac{1}{3}=\frac{10}{21}\div\frac{15}{28}\)
b,\(\frac{2}{7}\div y=\frac{10}{21}\times\frac{9}{14}\)
\(\frac{2}{7}:y=\frac{10}{21}.\frac{9}{14}\)
\(\frac{2}{7}:y=\frac{15}{49}\)
\(y=\frac{2}{7}:\frac{15}{49}\)
\(y=\frac{2}{7}.\frac{49}{15}\)
\(y=\frac{14}{15}\)
\(y-\frac{1}{3}=\frac{10}{21}:\frac{15}{28}\)
\(y-\frac{1}{3}=\frac{10}{21}.\frac{28}{15}\)
\(y-\frac{1}{3}=\frac{8}{9}\)
\(y=\frac{8}{9}+\frac{1}{3}\)
\(y=\frac{8}{9}+\frac{3}{9}\)
\(y=\frac{11}{9}\)
a) Ta có : \(y-\frac{1}{3}=\frac{10}{21}\div\frac{15}{28}\)
\(\Rightarrow\) \(y-\frac{1}{3}=\frac{8}{9}\)
\(\Rightarrow\) \(y\) \(=\frac{8}{9}+\frac{1}{3}\)
\(\Rightarrow\) \(y\) \(=\frac{11}{9}\)
Vậy \(y=\frac{11}{9}\)
b) Ta có : \(\frac{2}{7}\div y=\frac{10}{21}\times\frac{9}{14}\)
\(\Rightarrow\) \(\frac{2}{7}\div y=\frac{15}{49}\)
\(\Rightarrow\) \(y=\frac{2}{7}\div\frac{15}{49}\)
\(\Rightarrow\) \(y=\frac{14}{15}\)
Vậy \(y=\frac{14}{15}\)
Cbht !!!