`(x^2 - 5x + 7)^2 - (2x - 5)^2 = 0`
`<=> x^4 + 25^2 + 49 - 10x^3 - 70x + 14x^2 - (4x^2 - 20x + 25) = 0`
`<=> x^4 - 10x^3 + 39x^2 - 70x + 49 - 4x^2 + 20x - 25 = 0`
`<=> x^4 - 10x^3 + 35x^2 - 50x + 24 = 0`
`<=> x^4 - 4x^3 - 6x^3 + 24x^2 + 11x^2 - 44x - 6x + 24 = 0`
`<=> (x - 4)(x^3 - 6x^2 + 11x - 6) = 0`
`<=> (x - 4)(x^3 - 3x^2 - 3x^2 + 9x + 2x - 6) = 0`
`<=> (x - 4)(x - 3)(x^2 - 3x + 2) = 0`
`<=> (x - 4)(x - 3)(x - 2)(x - 1) = 0`
`<=> x ∈ {4,3,2,1}`
Vậy `S = {4; 3; 2; 1}`
\(\left(x^2-5x+7\right)^2-\left(2x-5\right)^2=0\)
\(\Leftrightarrow\left(x^2-5x+7\right)^2=\left(2x-5\right)^2\)
\(\Leftrightarrow\left|x^2-5x+7\right|=\left|2x-5\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x+7=-2x+5\\x^2-5x+7=2x-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-3x+2=0\\x^2-7x+12=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=2\\x=1\end{matrix}\right.\\\left[{}\begin{matrix}x=4\\x=3\end{matrix}\right.\end{matrix}\right.\)
\((x^2-5x+7)^2-(2x-5)^2=0 \)
\(⇔(x^2-5x+7+2x-5)(x^2-5x+7-2x+5)=0 \)
\(⇔(x^2-3x+2)(x^2-7x+12)=0 \)
\(⇔(x^2-2x-x+2)(x^2-3x-4x+12)=0 \)
\(⇔[x(x-2)-(x-2)][x(x-3)-4(x-3)]=0 \)
\(⇔(x-1)(x-2)(x-3)(x-4)=0\)
Vậy\(S=\) \(\left\{1;2;3;4\right\}\)
