Đáp án + Giải thích các bước giải :
`a)` `(x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15`
`<=>x^3-9x^2+27x-27-(x^3-27)+9(x^2+2x+1)=15`
`<=>x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15`
`<=>45x+9=15`
`<=>45x=6`
`<=>x=6/45=2/15`
Vậy `S={2/15}`
`b)` `4x^2-81=0`
`<=>(2x)^2-9^2=0`
`<=>(2x-9)(2x+9)=0`
`<=>`\(\left[ \begin{array}{l}2x-9=0\\2x+9=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{9}{2}\\x=-\dfrac{9}{2}\end{array} \right.\)
Vậy `S={9/2;-9/2}`
`c)` `x(x-5)(x+5)-(x-2)(x^2+2x+4)=3`
`<=>x(x^2-25)-(x^3-8)=3`
`<=>x^3-25x-x^3+8=3`
`<=>-25x+8=3`
`<=>-25x=-5`
`<=>x=5/25=1/5`
Vậy `S={1/5}`
`d)` `25x^2-2=0`
`<=>(5x)^2-(sqrt2)^2=0`
`<=>(5x-sqrt2)(5x+sqrt2)=0`
`<=>`\(\left[ \begin{array}{l}5x-\sqrt{2}=0\\5x+\sqrt{2}=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{\sqrt{2}}{5}\\x=-\dfrac{\sqrt{2}}{5}\end{array} \right.\)
Vậy `S={sqrt2/5,-sqrt2/5}`
`e)` `(x+2)^2=(2x-1)^2`
`<=>(x+2)^2-(2x-1)^2=0`
`<=>[(x+2)-(2x-1)][(x+2)+(2x-1)]=0`
`<=>(x+2-2x+1)(x+2+2x-1)=0`
`<=>(3-x)(3x+1)=0`
`<=>`\(\left[ \begin{array}{l}3-x=0\\3x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-\dfrac{1}{4}\end{array} \right.\)
Vậy `S={3;-1/4}`
`f)` `(x+2)^2-x+4=0`
`<=>x^2+4x+4-x+4=0`
`<=>x^2+3x+8=0`
Vì `x^2+3x+8=[x^2+2*x*3/2+(3/2)^2]+23/4`
`=(x+3/2)^2+23/4>=23/4forallx`
`->` Không tìm được nghiệm của phương trình
Vậy `S=emptyset`.
