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a/ Áp dụng tính chất của dãy tỉ số bằng nhau, có:
\(\frac{x}{6}=\frac{y}{4}=\frac{z}{3}=\frac{x+y-z}{6+4-3}=\frac{21}{7}=3\)
Suy ra: \(\frac{x}{6}=3\Rightarrow x=6\cdot3=18\)
\(\frac{y}{4}=3\Rightarrow y=3\cdot4=12\)
\(\frac{z}{3}=3\Rightarrow z=3\cdot3=9\)
Vậy x = 18, y = 12, z = 9
b/ Ta có: 3x = 2y => x/2 = y/3 => \(\frac{x^2}{2^2}=\frac{y^2}{3^2}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, có:
\(\frac{x^2}{2^2}=\frac{y^2}{3^2}=\frac{x^2-y^2}{2^2-3^2}=?\)
đề thiếu
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Ta có: \(\left(-\frac{1}{2}x^3y^4\right)-3x^2y\cdot\left(-\frac{5}{4}x^4y^7\right)-\frac{3}{4}x^6y^8\)
\(=-\frac{1}{2}x^3y^4+\frac{15}{4}x^6y^8-\frac{3}{4}x^6y^8\)
\(=-\frac{1}{2}x^3y^4+3x^6y^8\)
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a>x+y=5=> y=5-x
\(!x+1!+!3-x!\ge!x+1+3-x!=4\)
đẳng thức khi -1<=x<=3
=> xem lại đề
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Câu 1: Đề thiếu
Câu 2: D
Câu 3: C
Câu 4: B
Câu 5: C
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A+B+C
\(=5x^2y^3-6xy^4+5x^3y-1+-x^3y-7x^2y^3+5-xy^4+2x^2y^3-7xy^4-6\)
\(=-14xy^4+4x^3y-2\)
A-B-C
\(=5x^2y^3-6xy^4+5x^3y-1+x^3y+7x^2y^3-5+xy^4-2x^2y^3+7xy^4+6\)
\(=10x^2y^3+2xy^4+6x^3y\)
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Bài 1:
a) \(x^2+10x+26+y^2+2y=(x^2+10x+25)+(y^2+2y+1)\)
..................................................= \(\left(x+5\right)^2+\left(y+1\right)^2\)
b) \(z^2-6z+5-t^2-4t=(z^2-6t+9)-(t^2+4t+4)\)
............................................= \(\left(z-3\right)^2-\left(t+2\right)^2\)
c) \(x^2-2xy+2y^2+2y+1=(x^2-2xy+y^2)+(y^2+2y+1)\)
..................................................= \(\left(x-y\right)^2+\left(y+1\right)^2\)
d) \(4x^2-12x-y^2+2y+8=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)
.................................................= \(\left(2x-3\right)^2-\left(y-1\right)^2\)
Bài 2:
a) \(\left(x+y+4\right)\left(x+y-4\right)=\left(x+y\right)^2-16\)
b) \(\left(x-y+6\right)\left(x+y-6\right)=x^2-\left(y-6\right)^2\)
c) \(\left(y+2z-3\right)\left(y-2z+3\right)=y^2-\left(2z-3\right)^2\)
d) \(\left(x+2y+3z\right)\left(2y+3z-x\right)=\left(2y+3z\right)^2-x^2\)
a). x^4 = x^7
=> x = \(\orbr{\begin{cases}0\\1\end{cases}}\)
b) (2y+1)^6 = (2y+1)^8
=> \(\orbr{\begin{cases}2y+1=0\\2y+1=1\end{cases}}\)
=> \(\orbr{\begin{cases}y=-\frac{1}{2}\\y=0\end{cases}}\)
`a,`
`x^4=x^7`
`->x^4-x^7=0`
`->x^4 (1 - x^3)=0`
TH1 : `x^4=0 ->x=0`
TH2 : `1-x^3=0 ->x^3=1^3 ->x=1`
Vậy `x=0,x=1`
`b,`
`(2y+1)^6 = (2y+1)^8`
`-> (2y+1)^6 - (2y+1)^8=0`
`-> (2y+1)^6 [1-(2y+1)^2]=0`
TH1 : `(2y+1)^6 =0 ->2y+1=0 ->y=(-1)/2`
TH2 : `1 - (2y+1)^2=0`
`-> (2y+1)^2=1`
`-> 2y+1=1` hoặc `2y+1=-1`
`->y=0` hoặc `y=-1`
Vậy `y=0,y=-1,y=(-1)/2`