Đáp án + Giải thích các bước giải:
Câu `1` :
`(x+3)^3-x(3x+1)^2+(2x+1)(4x^2+1-2x)-3x^2=54`
`<=>x^3+9x^2+27x+27-x(9x^2+6x+1)+(2x+1)(4x^2-2x+1)-3x^2=54`
`<=>x^3+9x^2+27x+27-9x^3-6x^2-x+(2x)^3+1-3x^2=54`
`<=>x^3+9x^2+27x+27-9x^3-6x^2-x+8x^3+1-3x^2=54`
`<=>(x^3-9x^3+8x^3)+(9x^2-6x^2-3x^2)+(27x-x)+(27+1)=54`
`<=>26x+28=54`
`<=>26x=26<=>x=1`
Vậy `S={1}`
Câu `2` :
`14x^2(2x-1)+21x(1-2x)=0`
`<=>14x^2(2x-1)-21x(2x-1)=0`
`<=>(2x-1)(14x^2-21x)=0`
`<=>(2x-1)7x(2x-3)=0`
`<=>`\(\left[ \begin{array}{l}2x-1=0\\7x=0\\2x-3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=0\\x=\dfrac{3}{2}\end{array} \right.\)
Vậy `S={1/2;0;3/2}`
Câu `3` :
`5x(x-1)^5=10x^3(1-x)^3`
`<=>5x(x-1)^5-10x^3(1-x)^3=0`
`<=>5x(x-1)^5+10x^3(x-1)^3=0`
`<=>(x-1)^3[5x(x-1)^2+10x^3]=0`
`<=>(x-1)^3[5x(x^2-2x+1)+10x^3]=0`
`<=>(x-1)^3(5x^3-10x^2+5x+10x^3)=0`
`<=>(x-1)^3(15x^3-10x^2+5x)=0`
`<=>(x-1)^3*5x(3x^2-2x+1)=0`
`<=>[((x-1)^3=0),(5x=0),(3x^2-2x+1=0):}`
`<=>[(x-1=0),(x=0),(3x^2-2x+1=0):}`
`<=>[(x=1),(x=0),(x=emptyset):}`
Vậy `S={1;0}`.
