a)y^2-x^2-2x-1 b)5x^2+10x c)x(x-2)+3x-6 d)x^2-4x+4-y^2 e)x(x+4)-x^2=20 f)x(x-2)-3(x-2)=0

2 bình luận về “a)y^2-x^2-2x-1 b)5x^2+10x c)x(x-2)+3x-6 d)x^2-4x+4-y^2 e)x(x+4)-x^2=20 f)x(x-2)-3(x-2)=0”

1. $a,y²−x²−2x−1$$\\$ $=y²−(x²+2x+1)$$\\$ $=y²−(x+1)²$$\\$$=(y−x−1)(y+x+1)$$\\$

   $b,5x²+10x$$\\$ $=5x.x+5x.2$$\\$ $=5x(x+2)$$\\$

   $c,x(x−2)+3x−6$$\\$ $=x(x−2)+3(x−2)$$\\$ $=(x−2)(x+3)$$\\$

   $d,x²−4x+4−y²$$\\$ $=(x²−4x+4)−y²$$\\$ $=(x−2)²−y²$$\\$ $=(x−y−2)(x+y−2)$$\\$

   $e,x(x+4)−x²=20$$\\$ $⇒x²+4x−x²=20$$\\$ $⇒4x=20$$\\$ $⇒x=5$$\\$ $Vậy$ $x=5$$\\$

   $f,x(x−2)−3(x−2)=0$$\\$ $⇒(x−2)(x−3)=0$$\\$ $⇒x−2=0$ $hoặc$ $x−3=0$$\\$ $⇒x=2$ $hoặc$ $x=3$$\\$ $Vậy$ $x∈{(2,3)}$

    

   Trả lời
2. a, y^2 – x^2 – 2x – 1

   = y^2 – (x^2 + 2x + 1)

   = y^2 – (x + 1)^2

   = (y – x – 1)(y + x + 1)

   b, 5x^2 + 10x

   = 5x.x + 5x.2

   = 5x(x + 2)

   c, x(x -2) + 3x -6

   = x(x – 2) + 3(x – 2)

   = (x – 2)(x + 3)

   d, x^2 – 4x + 4 – y^2

   = (x^2 – 4x + 4) – y^2

   = (x – 2)^2 – y^2

   = (x – y – 2)(x + y – 2)

   e, x(x + 4) – x^2 = 20

   => x^2 + 4x – x^2 = 20

   => 4x = 20

   => x =5

   Vậy x = 5

   f, x(x – 2) – 3(x – 2) = 0

   => (x – 2)(x – 3) = 0

   => x – 2 =0 hoặc x – 3= 0

   => x = 2 hoặc x = 3

   Vậy x \in {2,3}
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