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1.X2-2X-4y2-4y
=x2-2x+1-(4y2+4y+1)
=(x+1)2-(2y+1)2
=>(x+1-2y-1)(x+1+2y+1)
=(x-2y)(x+2y+2)
2.x4+2x3-4x-4
=(x2)2-22+2x3-4x
=(x2-2)(x2+2)+2x(x2-2)
=(x2-2)(x2+2+2x)
a) \(2\left(x-1\right)^2+\left(x+3\right)^2=3\left(x-2\right)\left(x+1\right)\)
\(\Leftrightarrow2x^2-4x+2+x^2+6x+9=3x^2-3x-6\)
\(\Leftrightarrow5x=-17\)
\(\Rightarrow x=-\frac{17}{5}\)
b) \(\left(x+2\right)^2-2\left(x-3\right)=\left(x+1\right)^2\)
\(\Leftrightarrow x^2+4x+4-2x+6=x^2+2x+1\)
\(\Leftrightarrow10=1\)
=> vô nghiệm
c) \(\left(x-1\right)^2+\left(x-2\right)^2=2\left(x+4\right)^2-\left(22x+27\right)\)
\(\Leftrightarrow x^2-2x+1+x^2-4x+4=2x^2+8x+8-22x-27\)
\(\Leftrightarrow8x=-24\)
\(\Rightarrow x=-3\)
a) 2( x - 1 )2 + ( x + 3 )2 = 3( x - 2 )( x + 1 )
<=> 2( x2 - 2x + 1 ) + x2 + 6x + 9 = 3( x2 - x - 2 )
<=> 2x2 - 4x + 2 + x2 + 6x + 9 = 3x2 - 3x - 6
<=> 2x2 - 4x + x2 + 6x - 3x2 + 3x = -6 - 2 - 9
<=> 5x = -17
<=> x = -17/5
b) ( x + 2 )2 - 2( x - 3 ) = ( x + 1 )2
<=> x2 + 4x + 4 - 2x + 6 = x2 + 2x + 1
<=> x2 + 4x - 2x - x2 - 2x = 1 - 4 - 6
<=> 0x = -9 ( vô lí )
Vậy phương trình vô nghiệm
c) ( x - 1 )2 + ( x - 2 )2 = 2( x + 4 )2 - ( 22x + 27 )
<=> x2 - 2x + 1 + x2 - 4x + 4 = 2( x2 + 8x + 16 ) - 22x - 27
<=> 2x2 - 6x + 5 = 2x2 + 16x + 32 - 22x - 27
<=> 2x2 - 6x - 2x2 - 16x + 22x = 32 - 27 - 5
<=> 0x = 0 ( đúng ∀ x ∈ R )
Vậy phương trình nghiệm đúng ∀ x ∈ R
TL:
\(3,3x^2-6xy+3y^2\)
\(=3\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)^2\)
a) ( x - 3 )3 - ( x - 3 )( x2 + 3x + 9 ) + 9( x + 1 )2 = 4
<=> x3 - 9x2 + 27x - 27 - ( x3 - 27 ) + 9( x2 + 2x + 1 ) = 4
<=> x3 - 9x2 + 27x - 27 - x3 + 27 + 9x2 + 18x + 9 = 4
<=> 45x + 9 = 4
<=> 45x = -5
<=> x = -5/45 = -1/9
b) x( x - 5 )( x + 5 ) - ( x + 2 )( x2 - 2x + 4 ) = 17
<=> x( x2 - 25 ) - ( x3 + 8 ) = 17
<=> x3 - 25x - x3 - 8 = 17
<=> -25x - 8 = 17
<=> -25x = 25
<=> x = -1
( 2x + 1 )2 - 4x( x - 1 ) = 5
<=> 4x2 + 4x + 1 - 4x2 + 4x = 5
<=> 8x + 1 = 5
<=> 8x = 4
<=> x = 4/8 = 1/2
\(1,3x\left(x-2\right)-2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
\(2,5x\left(x-3\right)+\left(x-3\right)\)
\(=\left(5x-1\right)\left(x-3\right)\)
\(3,5x\left(x-3\right)-x+3\)
\(=\left(5x-1\right)\left(x-3\right)\)
\(4,x^2-4+3y\left(x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)+3y\left(x+2\right)\)
\(=\left(x+2\right)\left(x-2+3y\right)\)
1) 3x(x-2) - 2(x-2)=(x-2)(3x-2)
2) 5x(x-3) +x-3=5x(x-3)+(x-3)=(x-3)(5x+1)
3) 5x(x-3) - x+3=5x(x-3) -(x-3)=(x-3)(5x-1)
4) x^2 -4+3y(x+2)=(x^2-4)+3y(x+2)=(x-2)(x+2)+3y(x+2)=(x+2)(x-2+3y)
Hok tốt nha!!!=.=