Đáp án + Giải thích các bước giải:
`a)` `x^2-10x=-25`
`<=>x^2-10x+25=0`
`<=>x^2-2*x*5+5^2=0`
`<=>(x-5)^2=0`
`<=>x-5=0<=>x=5`
Vậy `S={5}`
`b)` `4x^2-4x=-1`
`<=>4x^2-4x+1=0`
`<=>(2x)^2-2*2x*1+1^2=0`
`<=>(2x-1)^2=0`
`<=>2x-1=0<=>x=1/2`
Vậy `S={1/2}`
`c)` `(1-2x)^2=(3x-2)^2`
`<=>(1-2x)^2-(3x-2)^2=0`
`<=>(1-2x-3x+2)(1-2x+3x-2)=0`
`<=>(3-5x)(x-1)=0`
`<=>`\(\left[ \begin{array}{l}3-5x=0\\x-1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{3}{5}\\x=1\end{array} \right.\)
Vậy `S={3/5;1}`
`d)` `(x-2)^3+(5-2x)^3=0`
`<=>(x-2+5-2x)[(x-2)^2-(x-2)(5-2x)+(5-2x)^2]=0`
`<=>(3-x)[x^2-4x+4-(5x-2x^2-10+4x)+25-20x+4x^2]=0`
`<=>(3-x)(x^2-4x+4-5x+2x^2+10-4x+25-20x+4x^2)=0`
`<=>(3-x)(7x^2-33x+39)=0`
`<=>3-x=0`
`<=>x=3`
(Vì `7x^2-33x+39=7(x^2-33/7x+39/7)`
`=7[x^2-2*x*33/14+(33/14)^2]+3/28`
`=7(x-33/14)^2+3/28>=3/28>0`
`->` Vô nghiệm).
