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cậu ơi đè cậu là :
x + ( x + 1 ) + ( x + 2 ) + .... +(x+ 19 )+ (x+20) +(x+ 21) = 0
hay thế này : x + ( x + 1 ) + ( x + 2 ) + 3+.... + 19 + 20 + 21 = 0 ?
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Câu 1 : \(\frac{x+2}{18}+\frac{x+2}{19}+\frac{x+2}{20}=\frac{x+2}{21}+\frac{x+2}{22}\)
=> \(\frac{x+2}{18}+\frac{x+2}{19}+\frac{x+2}{20}-\frac{x+2}{21}-\frac{x+2}{22}=0\)
=> x+2 . ( \(\frac{1}{18}+\frac{1}{19}+\frac{1}{20}-\frac{1}{21}-\frac{1}{22}\)) = 0
Vì \(\frac{1}{18}+\frac{1}{19}_{ }+\frac{1}{20}-\frac{1}{21}-\frac{1}{22}\ne0\)nên x+2=0
=> x= 0 - 2 = -2
Vậy x = -2
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\(\frac{-2}{7}\div\frac{15}{14}=\frac{-21}{20}\div\left(5\times x\right)\)
\(\Rightarrow\frac{-4}{15}=\frac{-21}{20}\div\left(5\times x\right)\)
\(\Rightarrow5\times x=\frac{-21}{20}\div\frac{-4}{15}\)
\(\Rightarrow5\times x=\frac{63}{16}\)
\(\Rightarrow x=\frac{63}{16}\div5\)
\(\Rightarrow x=\frac{63}{80}\)
~ học tốt nha ~
\(\frac{-2}{7}:\frac{15}{14}=\frac{-21}{20}:(5\cdot x)\)
\(\Leftrightarrow\frac{-21}{20}:(5\cdot x)=\frac{-2}{7}:\frac{15}{14}\)
\(\Leftrightarrow\frac{-21}{20}:(5\cdot x)=\frac{-2}{7}\cdot\frac{14}{15}\)
\(\Leftrightarrow\frac{-21}{20}:(5\cdot x)=\frac{-2}{1}\cdot\frac{2}{15}\)
\(\Leftrightarrow\frac{-21}{20}:(5\cdot x)=\frac{4}{15}\)
\(\Leftrightarrow5\cdot x=\frac{-21}{20}:\frac{4}{15}\)
\(\Leftrightarrow5\cdot x=\frac{-21}{20}\cdot\frac{15}{4}\)
\(\Leftrightarrow5\cdot x=\frac{-21}{4}\cdot\frac{3}{4}\)
\(\Leftrightarrow5\cdot x=\frac{-63}{16}\)
\(\Leftrightarrow x=\frac{-63}{16}:5\)
\(\Leftrightarrow x=\frac{-63}{16}\cdot\frac{1}{5}=\frac{-63}{80}\)
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\(\left(\frac{x}{20}+1\right)+\left(\frac{x-1}{21}+1\right)=\left(\frac{x-2}{22}+1\right)+\left(\frac{x-3}{23}+1\right)\)
\(\frac{x+20}{20}+\frac{x+20}{21}-\frac{x+20}{22}-\frac{x+20}{23}=0\)
\(\left(x+20\right).\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)=0\)
mà \(\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)\ne0\)
=> x+20=0 => x=-20
vậy x=-20
\(\frac{x}{20}+\frac{x-1}{21}=\frac{x-2}{22}+\frac{x-3}{23}\)
\(1+\frac{x}{20}+1+\frac{x-1}{21}=1+\frac{x-2}{22}+1+\frac{x-3}{23}\)
\(\frac{x+20}{20}+\frac{21+x-1}{21}=\frac{22+x-2}{22}+\frac{23+x-3}{23}\)
\(\frac{x+20}{20}+\frac{x+20}{21}=\frac{x+20}{22}+\frac{x+20}{23}\)
\(\frac{x+20}{20}+\frac{x+20}{21}-\frac{x+20}{22}-\frac{x+20}{23}=0\)
\(\left(x+20\right)\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)=0\)
Mà \(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\ne0\)
\(\Rightarrow x+20=0\)
\(\Rightarrow x=-20\)
Vậy x = -20
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Giải:
1. Theo tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{-21}{7}=-3\)
+) \(\frac{x}{2}=-3\Rightarrow x=-6\)
+) \(\frac{y}{5}=-3\Rightarrow y=-15\)
Vậy x = -6
y = -15
2. Ta có:
\(7x=3y\Rightarrow\frac{7x}{21}=\frac{3y}{21}=\frac{x}{3}=\frac{y}{7}\)
Theo tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{3}=\frac{y}{7}=\frac{x-y}{3-7}=\frac{16}{-4}=-4\)
+) \(\frac{x}{3}=-4\Rightarrow x=-12\)
+) \(\frac{y}{7}=-4\Rightarrow y=-28\)
Vậy x = -12
y = -28
1/ \(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=-\frac{21}{7}=-3\)
\(\frac{x}{2}=-3\Rightarrow x=-6\)
\(\frac{x}{5}=-3\Rightarrow x=-15\)
2/ \(7x=3y\Rightarrow\frac{x}{7}=\frac{y}{3}\)
\(\frac{x}{7}=\frac{y}{3}=\frac{x-y}{7-3}=\frac{16}{4}=4\)
\(\frac{x}{7}=4\Rightarrow x=28\)
\(\frac{y}{3}=4\Rightarrow y=12\)
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+) Xét \(x=0\)
\(\Rightarrow\left(3y+1\right)\left(y+1\right)=21\)
\(\Rightarrow3y+1;y+1\inƯ\left(21\right)=\left\{\pm1;\pm3;\pm7;\pm21\right\}\)
Mà \(3y+1\) chia \(3\) dư \(1;-2\)
\(\Rightarrow3y+1\in\left\{1;-2;7\right\}\)
\(\Rightarrow y\in\left\{0;-1;2\right\}\)
+) Với \(y=0\)
\(\Rightarrow y+1=1\) ( loại )
+) Với \(y=-1\)
\(\Rightarrow y+1=0\) ( loại )
+) Với \(y=2\)
\(\Rightarrow y+1=3\) ( thỏa mãn )
+) Xét \(x\ne0\)
\(\Rightarrow2^{\left|x\right|}+x\left(x+1\right)\) chẵn
\(\Rightarrow y\) lẻ
\(\Rightarrow2x+3y+1\) chẵn
Mà \(21\) lẻ
\(\Rightarrow x\ne0\) phương trình vô nghiệm
Vậy \(\left(x;y\right)=\left(0;2\right)\)
Đặt \(t=x-20\)
Suy ra : \(t^2+\left(t-1\right)^2=1\)
\(\Leftrightarrow t^2+t^2-2t+1=1\)
\(\Leftrightarrow2t^2-2t=0\)
\(\Leftrightarrow2t\left(t-1\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}t=0\\t=1\end{cases}\Rightarrow\hept{\begin{cases}x=20\\x=21\end{cases}}}\)
Vậy x=20 và x=21