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Vd là Hình chữ nhật là có cả đối xứng trục và đối xứng tâm
Hình vuông cũng vậy
Hình thang cân thì có đối xứng trục nhưng không có đối xứng tâm
`a)2x^2+3(x-1)(x+1)=5x(x+1)`
`<=>2x^2+3x^2-3=5x^2+5x`
`<=>5x=-3`
`<=>x=-3/5`
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`b)(x-3)^3+3-x=0` nhỉ?
`<=>(x-3)^3-(x-3)=0`
`<=>(x-3)(x^2-1)=0`
`<=>[(x=3),(x^2=1<=>x=+-1):}`
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`c)5x(x-2000)-x+2000=0`
`<=>5x(x-2000)-(x-2000)=0`
`<=>(x-2000)(5x-1)=0`
`<=>[(x=2000),(x=1/5):}`
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`d)3(2x-3)+2(2-x)=-3`
`<=>6x-9+4-2x=-3`
`<=>4x=2`
`<=>x=1/2`
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`e)x+6x^2=0`
`<=>x(1+6x)=0`
`<=>[(x=0),(x=-1/6):}`
11)\(\dfrac{3x+1}{x-5}+\dfrac{2x}{x-5}=\dfrac{3x+2x+1}{x-5}=\dfrac{5x+1}{x-5}\)
12)\(\dfrac{4-x^2}{x-3}+\dfrac{2}{x^2-9}=\dfrac{4-x^2}{x-3}+\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{\left(4-x^2\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{2+\left(2-x\right)\left(2+x\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
13)
\(\dfrac{3}{4x-2}+\dfrac{2x}{4x^2-1}=\dfrac{3}{2\left(2x-1\right)}+\dfrac{2x}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{3\left(2x+1\right)}{2\left(2x-1\right)\left(2x+1\right)}+\dfrac{2.2x}{2\left(2x-1\right)\left(2x+1\right)}=\dfrac{6x+3+4x}{2\left(2x-1\right)\left(2x+1\right)}=\dfrac{10x+3}{2\left(2x-1\right)\left(2x+1\right)}\)
14)
\(\dfrac{2x+1}{2x-4}+\dfrac{5}{x^2-4}=\dfrac{2x+1}{2\left(x-2\right)}+\dfrac{5}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(2x+1\right)\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\dfrac{5.2}{2\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2+5x+12}{2\left(x-2\right)\left(x+2\right)}\)
4.2:
a: x^2-x+1=x^2-x+1/4+3/4
=(x-1/2)^2+3/4>=3/4>0 với mọi x
=>x^2-x+1 ko có nghiệm
b: 3x-x^2-4
=-(x^2-3x+4)
=-(x^2-3x+9/4+7/4)
=-(x-3/2)^2-7/4<=-7/4<0 với mọi x
=>3x-x^2-4 ko có nghiệm
5:
a: x^2+y^2=25
x^2-y^2=7
=>x^2=(25+7)/2=16 và y^2=16-7=9
x^4+y^4=(x^2)^2+(y^2)^2
=16^2+9^2
=256+81
=337
b: x^2+y^2=(x+y)^2-2xy
=1^2-2*(-6)
=1+12=13
x^3+y^3=(x+y)^3-3xy(x+y)
=1^3-3*1*(-6)
=1+18=19
a) x^2 - x = 0
x(x-1)=0
x=0 hoặc x=1
b) (x-2)^2 - 3(x-2)=0
(x-2)(x-5)=0
x=2 hoặc x=5
c) pt <=> 3(x - 1) - 2(x - 1)=0
<=> x-1=0
<=> x = 1
a) \(\Rightarrow x\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
b) \(\Rightarrow\left(x-2\right)\left(x-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)
c) \(\Rightarrow3\left(x-1\right)-2\left(x-1\right)=0\)
\(\Rightarrow x-1=0\Rightarrow x=1\)
d) \(\Rightarrow\left(x-5\right)\left(x+5\right)+\left(x-5\right)^2=0\)
\(\Rightarrow\left(x-5\right).2x=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
e) \(\Rightarrow\left(x-1\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
1. x2-x-2
=(x2-2x)+(x-2)
= x(x-2)+(x-2)
= (x+1)(x-2)
2.x2-3x+2
=x2-x-2x+2
=(x2-x)-(2x-2)
=x(x-1)-2(x-1)
=(x-2)(x-1)
3.-x2-2x+3
=3-2x-x2
=3+x-3x-x2
=(3+x)-(3x+x2)
=(3+x)-x(3+x)
=(1-x)(3+x)
4. x2-5x+4
=x2-x-4x+4
=(x2-x)-(4x-4)
=x(x-1)-4(x-1)
=(x-1)(x-4)
5. x2-5x+6
=x2-2x-3x+6
=(x2-2x)-(3x-6)
=x(x-2)-3(x-2)
=(x-2)(x-3)
6.x2-6x+5
=(x2-x)-(5x-5)
=x(x-1)-5(x-1)
=(x-1)(x-5)
7.x2-7x+12
=(x2-3x)-(4x-12)
=x(x-3)-4(x-3)
=(x-4)(x-3)
8.-x2+7x-12
=(-x2+3x)+(4x-12)
=-x(x-3)+4(x-3)
=(4-x)(x-3)
9.x2-3x-4
=(x2+x)-(4x+4)
=x(x+1)-4(x+1)
=(x-4)(x+1)
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