Đáp án:
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`1,`
`a^4 - b^2 (2a-b)^2`
`= a^4 - [b^2 (2a-b)^2]`
`= a^4 - [b (2a-b)]^2`
`= a^4 - [2ab - b^2]^2`
`= (a^2)^2 - [2ab - b^2]^2`
`= [a^2 - (2ab - b^2)] [a^2 + (2ab - b^2)]`
`= [a^2 - 2ab + b^2] [a^2 + 2ab - b^2]`
`= (a-b)^2 [a^2 + 2ab - b^2]`
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`2,`
`a,`
`(5x-4)^2 - 49x^2 = 0`
`↔ (5x-4)^2 - (7x)^2=0`
`↔ [(5x-4)-7x] [(5x-4)+7x]=0`
`↔ [5x-4-7x][5x-4+7x]=0`
`↔ [-2x-4] [12x - 4]=0`
`↔` \(\left[ \begin{array}{l}-2x-4=0\\12x-4=0\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}-2x=4\\12x=4\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=-2\\x=\dfrac{1}{3}\end{array} \right.\)
Vậy `S= {-2;1/3}`
`b,`
`(6x+1)^2 - (x+1)^2=0`
`↔ [(6x+1) - (x+1)] [(6x+1) + (x+1)]=0`
`↔ [6x+1-x-1] [6x+1+x+1]=0`
`↔ [(6x-x)+(1-1)] [(6x+x) + (1+1)]=0`
`↔ 5x [7x+2]=0`
`↔` \(\left[ \begin{array}{l}5x=0\\7x+2=0\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=0\\7x=-2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=0\\x=\dfrac{-2}{7}\end{array} \right.\)
Vậy `S = {0; (-2)/7}`
