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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
a, Thay \(x=\frac{7}{13}\)vào \(x+y=40\)=> \(\frac{7}{13}+y=40\Rightarrow y=40-\frac{7}{13}\Rightarrow y=\frac{513}{13}\)
b, Ta có: \(13x=7y\Rightarrow\frac{x}{7}=\frac{y}{13}\)và x+y=-60. Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{7}=\frac{y}{13}=\frac{x+y}{7+13}=\frac{-60}{20}=-3\) \(\Rightarrow\hept{\begin{cases}\frac{x}{7}=-3\Rightarrow x=-3\cdot7=-21\\\frac{y}{13}=-3\Rightarrow y=-3\cdot13=-39\end{cases}}\)
\(\frac{x^2}{9}=\frac{9^2}{18}\)
\(\frac{x^2}{9}=\frac{\left(3^2\right)^2}{18}\)
\(\frac{x^2}{9}=\frac{3^{2.2}}{18}\)
\(\frac{x^2}{9}=\frac{3^4}{18}\)
\(\frac{x^2}{9}=\frac{3^4}{2.3^2}\)
\(\frac{x^2}{9}=\frac{3^4}{2.3^2}\)
\(\frac{x^2}{9}=\frac{3^{4-2}}{2}\)
\(\frac{x^2}{9}=\frac{3^2}{2}\)
\(\frac{x^2}{3^2}=\frac{3^2}{2}\)
\(2\left(x^2\right)=9\left(3^2\right)\)
\(\frac{2\left(x^2\right)}{2}=\frac{9\left(3^2\right)}{2}\)
\(x^2=\frac{3^2.3^2}{2}\)
\(x^2=\frac{3^{2+2}}{2}\)
\(x^2=\frac{3^4}{2}\)
\(\left(x^2\right)^{\frac{1}{2}}=\left(\frac{3^4}{2}\right)^{\frac{1}{2}}\)
\(x^{2.\frac{1}{2}}=\frac{\left(3^4\right)^{\frac{1}{2}}}{2^{\frac{1}{2}}}\)
\(x^{\frac{2}{2}}=\frac{3^{4.\frac{1}{2}}}{2^{\frac{1}{2}}}\)
\(x=\frac{3^{\frac{4}{2}}}{2^{\frac{1}{2}}}\)
\(x=\frac{3^{\frac{2^2}{2}}}{2^{\frac{1}{2}}}\)
\(x=\frac{3^{2^{2-1}}}{2^{\frac{1}{2}}}\)
\(x=\frac{3^2}{2^{\frac{1}{2}}}\)
\(x=\frac{9}{2^{\frac{1}{2}}}\)
\(x=\frac{9}{\frac{5}{2}}\)
\(x=9:\left(5:2\right)\)
\(x=9:2,5\)
\(x=3,6\)
\(3,6^2+y^2=100\)
\(12,96+y^2=100\)
\(y^2=100-12,96\)
\(y^2=87,04\)
\(y=\sqrt{87,04}\)
b.
105 \(⋮\)x => x\(\in\)Ư(105)
126 \(⋮\)x => x\(\in\)Ư(126)
Suy ra x\(\in\)ƯC(105;126) = Ư(21)={1;3;7;21)
mà x>10
nên x=21
vì x chia hết cho 18,x chia hết cho 48
nên x thuộc BC(18,48)
ta có 18=2x3 mũ 2
48=2 mũ 4x3
suy ra BCNN(18,48)=2 mũ 4x 3 mũ 2=144
suy ra BC(18,48)=B(144)={0;144;288;...}
mà x thuộc BC(18,48)và 100<x<200
suy ra x=144
vậy x=144
40 . x = 100 . ( x - 18 )
40 x = 100 x - 1800
40x - 100x = -1800
- 60 x = - 1800
x = 30
40 . x = 100 . ( x - 18 )
40 x = 100 x - 1800
40x - 100x = -1800
- 60 x = - 1800
x = 30