Tìm y .y+25nhân 3=204 . 462+ynhân 5=562
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Ta có : SSH từ 1 - 21 là : ( 21 - 1 ) : 1 x 1 +1 = 20
Tổng là : ( 21 + 1 ) x 20 : 2 = 220
Vậy 1 x y + 2 x y + 3 x y + 4 x y + ...... + 21 x y
= y x ( 1 + 2 + 3 + 4 + .... + 21 ) = 220 y
Vậy tổng trên = 220 y
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y x 500 = 780 000
y = 780 000 : 500
y = 1560
y x 120 = 12000
y = 12000 : 120
y = 100
y : 145 = 318
y = 318 x 145
y = 46110
y : 213 = 456
y = 456 x 213
y= 97128
y x 70 = 238
y = 238 : 70
y = 3.4
y x 78 = 936
y = 936 : 78
y = 12
462 : y = 66
y = 462 : 66
y = 7
709 : y = 82
y = 709 : 82
y = 8.64634146341
y x 500 = 780 000
y = 780 000 : 500
y = 1560
y x 120 = 12000
y = 12000 : 120
y = 100
y : 145 = 318
y = 318 x 145
y = 46110
y : 213 = 456
y = 456 x 213
y= 97128
y x 70 = 238
y = 238 : 70
y = 3.4
y x 78 = 936
y = 936 : 78
y = 12
462 : y = 66
y = 462 : 66
y = 7
709 : y = 82
y = 709 : 82
y = 8.64634146341
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\(\left(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+\frac{2}{17x19}+\frac{2}{19x21}\right)\)) x 462 - y = 19
\(=\left(\frac{13-11}{11x13}+\frac{15-13}{13x15}+\frac{17-15}{15x17}+\frac{19-17}{17x19}+\frac{21-19}{19x21}\right)\)x 462 - y = 19
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\)) x 462 - y = 19
\(=\left(\frac{1}{11}-\frac{1}{21}\right)\)x 462 - y = 19
\(=\left(\frac{21}{231}-\frac{11}{231}\right)\)x 462 - y = 19
\(=\frac{10}{231}\)x 462 - y = 19
\(=20\)- y = 19
y = 20 - 19
y = 1
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a)\(7y=5x\Rightarrow\frac{y}{5}=\frac{z}{7}\)
\(\Rightarrow\frac{x}{3}=\frac{y}{7}=\frac{z}{5}\)
Đặt dãy tỉ số bằng k rồi thay vào x+y-z=24
b) tương tự
a)\(\frac{x}{3}=\frac{y}{5};7x=5z;x+y-z=24\)
Ta có :
\(\frac{x}{3}=\frac{y}{5};\frac{y}{5}=\frac{z}{7}\Leftrightarrow\frac{x}{3}=\frac{y}{5}=\frac{z}{7}\)
Theo tính chất của dãy tỉ số bằng nhau ta có :
\(\frac{x}{3}=\frac{y}{5}=\frac{z}{7}=\frac{x+y-z}{3+5-7}=\frac{24}{1}=24\)
\(\Rightarrow\frac{x}{3}=24\Rightarrow x=24.3=72\)
\(y=24.5=120\)
\(z=24.7=168\)
b) Ta có : \(\frac{x+1}{3}=\frac{y+2}{4}=\frac{z+3}{5}\)và \(x+y+z=18\)
Theo tính chất của dãy tỉ số bằng nhau ta có :
\(\frac{x+1}{3}=\frac{y+2}{4}=\frac{z+3}{5}=\frac{\left(x+y+z\right)+\left(1+2+3\right)}{3+4+5}=\frac{24}{12}=2\)
\(\Rightarrow\frac{x+1}{3}=2\Rightarrow x=2.3-1=5\)
\(\Rightarrow\frac{y+2}{4}=2\Rightarrow y=2.4-2=6\)
\(\Rightarrow\frac{z+3}{5}=2\Rightarrow z=2.5-3=7\)
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\(y+25\times3=204\)
\(y+75=204\)
\(y=204-75=129\)
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\(462+y\times5=562\)
\(y\times5=562-462=100\)
`y=100:5=20`
y+25x3=204 462+y x 5 =562
y+25=204:3 462+y=562x5
y+25= 68 462+y=2810
y=68-25 y=2810-462
y=43 y=2348