Toán PTĐTTNT : a)x^2-xy-6y^2 b)x^3-3x^2-6x+8=0 17/09/2021 By Claire PTĐTTNT : a)x^2-xy-6y^2 b)x^3-3x^2-6x+8=0
$a)x^2-xy-6y^2\\ =x^2-3xy+2xy-6y^2 \\ =x(x-3y)+2y(x-3y) \\ =(x+2y)(x-3y) \\ b)x^3-3x^2-6x+8=0\\ \to x^3-x^2-2x^2+2x-8x+8=0\\ \to x^2(x-1)-2x(x-1)-8(x-1) =0 \\\to (x-1)(x^2-2x-8)=0\\\to(x-1)(x^2+2x-4x-8)=0\\\to(x-1)[x(x+2)-4(x+2)]=0\\\to(x-1)(x+2)(x-4)=0$\(\to\left[ \begin{array}{l}x-1=0\\x+2=0\\x-4=0\end{array} \right.\\\) \(\to\left[ \begin{array}{l}x=1\\x=-2\\x=4\end{array} \right.\) Trả lời
Đáp án: Giải thích các bước giải: a)3x^2-12x+12 =3x^2-6x-6x+12 =3x(x-2)-6(x-2) =(3x-6)(x-2) b)x^2-xy-6y^2 =x^2-3xy+2xy-6y^2 =x(x-3y)+2y(x-3y) =(x+2y)(x-3y) c)x^2+7x+7y-y^2 =x^2+xy-xy-y^2+7x+7y =x(x+y)-y(x+y)+7(x+y) =(x-y+7)(x+y) d)x^3-3x^2-6x+8=0 =x^3-3x^2-6x+8 =x^3-x^2-2x^2+2x-8x+8 = x(x-1)-2x(x-1)-8(x-1) = (x-1)(x-2x-8) Trả lời
$a)x^2-xy-6y^2\\ =x^2-3xy+2xy-6y^2 \\ =x(x-3y)+2y(x-3y) \\ =(x+2y)(x-3y) \\ b)x^3-3x^2-6x+8=0\\ \to x^3-x^2-2x^2+2x-8x+8=0\\ \to x^2(x-1)-2x(x-1)-8(x-1) =0 \\\to (x-1)(x^2-2x-8)=0\\\to(x-1)(x^2+2x-4x-8)=0\\\to(x-1)[x(x+2)-4(x+2)]=0\\\to(x-1)(x+2)(x-4)=0$\(\to\left[ \begin{array}{l}x-1=0\\x+2=0\\x-4=0\end{array} \right.\\\) \(\to\left[ \begin{array}{l}x=1\\x=-2\\x=4\end{array} \right.\)
Đáp án:
Giải thích các bước giải:
a)3x^2-12x+12
=3x^2-6x-6x+12
=3x(x-2)-6(x-2)
=(3x-6)(x-2)
b)x^2-xy-6y^2
=x^2-3xy+2xy-6y^2
=x(x-3y)+2y(x-3y)
=(x+2y)(x-3y)
c)x^2+7x+7y-y^2
=x^2+xy-xy-y^2+7x+7y
=x(x+y)-y(x+y)+7(x+y)
=(x-y+7)(x+y)
d)x^3-3x^2-6x+8=0
=x^3-3x^2-6x+8
=x^3-x^2-2x^2+2x-8x+8
= x(x-1)-2x(x-1)-8(x-1)
= (x-1)(x-2x-8)