Đáp án + Giải thích các bước giải:
`a, 4x^2 - 4x + 1 =0`
`<=> (2x-1)^2 = 0`
`<=> 2x - 1=0`
`<=> x= 1/2`
Vậy `x=-1/2`
`b, x^2 - 10x =-25`
`<=> x^2 - 10x + 25 = 0`
`<=> (x-5)^2 = 0`
`<=> x -5 =0`
`<=> x=5`
Vậy `x=5`
`c, -16x^2 + 8x = 1`
`<=> -16x^2 + 8x - 1=0`
`<=> -(16x^2 - 8x + 1)=0`
`<=> -(4x - 1)^2 = 0`
`<=> 1 - 4x = 0`
`<=> x = 1/4`
Vậy `x=1/4`
`d, (1-3x)^2 = 0,25`
`<=> (1-3x)^2 - (0,5)^2 = 0`
`<=> (1 - 3x + 0,5)(1-3x - 0,5)=0`
`<=> (1,5 - 3x)(0,5 - 3x)=0`
`<=> ` \(\left[ \begin{array}{l}1,5-3x=0 \\0,5 - 3x = \end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=1/2\\x=1/6\end{array} \right.\)
Vậy `x=1/2 ; x=1/6`
`e, (x-1)^2 = (2x+1)^2`
`<=> (x-1)^2 - (2x+1)^2 = 0`
`<=> (x-1-2x-1)(x-1+2x+1)=0`
`<=> (-x-2)(3x)=0`
`<=>` \(\left[ \begin{array}{l}-x-2=0\\3x=0\end{array} \right.\)
`<=> ` \(\left[ \begin{array}{l}x=-2\\x=0\end{array} \right.\)
Vậy `x=-2;x=0`
`g, 8 -12x + 6x^2 - x^3 = -27`
`<=> (2 - x)^3 = -3^3`
`=> 2 -x = -3`
`<=> x = 5`
Vậy `x=5`
