Đáp án `+` Giải thích các bước giải `!`
`1.`
`a)`
`xy-3x+2y^2-6y`
`= (xy-3x)+(2y^2-6y)`
`= x(y-3)+2y(y-3)`
`= (x+2y)(y-3)`
`b)`
`3x^2y^3+x^4y-3x^3y^2-xy^4`
`= xy(3xy^2+x^3-3x^2y-y^3)`
`= xy[(3xy^2-3x^2y)+(x^3-y^3)]`
`= xy[3xy(y-x)+(x-y)(x^2+xy+y^2)]`
`= xy[-3xy(x-y)+(x-y)(x^2+xy+y^2)]`
`= xy(x-y)(-3xy+x^2+xy+y^2)`
`= xy(x-y)(x^2-2xy+y^2)`
`= xy(x-y)(x-y)^2`
`= xy(x-y)^3`
`d)`
`x^3-2x^2-5x+6`
`= x^3-x^2-x^2+x-6x+6`
`= (x^3-x^2)-(x^2-x)-(6x-6)`
`= x^2(x-1)-x(x-1)-6(x-1)`
`= (x-1)(x^2-x-6)`
`= (x-1)(x^2-3x+2x-6)`
`= (x-1)[(x^2-3x)+(2x-6)]`
`= (x-1)[x(x-3)+2(x-3)]`
`= (x-1)(x+2)(x-3)`
`2.`
`a)`
`(x+2)(x^2-2x+4)-(x-3)(x^2-2x+1) = 5x^2`
`<=> x^3+8-x^3+2x^2-x+3x^2-6x+3 = 5x^2`
`<=> (x^3-x^3)+(2x^2+3x^2-5x^2)+(-x-6x)+(8+3) = 0`
`<=> -7x+11 = 0`
`<=> -7x = -11`
`<=> x = (11)/7`
Vậy `S= {(11)/7}`
`b)`
`(x^2-3)(x^2+3)+8(x^2-1)^2+3x^2+5 = 0`
`<=> x^4-9+8(x^4-2x^2+1)+3x^2+5 = 0`
`<=> x^4-9+8x^4-16x^2+8+3x^2+5 = 0`
`<=> (x^4+8x^4)+(-16x^2+3x^2)+(-9+8+5) = 0`
`<=> 9x^4-13x^2+4 = 0`
`<=> 9x^4-9x^2-4x^2+4 = 0`
`<=> (9x^4-9x^2)-(4x^2-4) = 0`
`<=> 9x^2(x^2-1)-4(x^2-1) = 0`
`<=> (9x^2-4)(x^2-1) = 0`
`<=> (3x-2)(3x+2)(x-1)(x+1) = 0`
`⇔` \(\left[ \begin{array}{l}3x-2=0\\3x+2=0\\x-1=0\\x+1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}3x=2\\3x=-2\\x=1\\x=-1\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=\dfrac{2}{3}\\x=-\dfrac{2}{3}\\x=1\\x=-1\end{array} \right.\)
Vậy `S= {2/3; -(2)/3; 1; -1}`
