a,
`(3x+1)(7x+3)=(5x-7)(3x+1)`
`<=>(3x+1)(7x+3)-(5x-7)(3x+1)=0`
`<=>(3x+1)(7x+3-5x+7)=0`
`<=>(3x+1)(2x+10)=0`
`<=>`\(\left[ \begin{array}{l}3x+1=0\\2x+10=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=-\dfrac13\\x=-5\end{array} \right.\)
Vậy `S={-5;-1/3}`
b,
`x^2+10x+25-4x(x+5)=0`
`<=>(x+5)^2-4x(x+5)=0`
`<=>(x+5)(x+5-4x)=0`
`<=>(x+5)(-3x+5)=0`
`<=>`\(\left[ \begin{array}{l}x+5=0\\-3x+5=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=-5\\x=\dfrac53\end{array} \right.\)
Vậy `S={-5;5/3}`
c,
`(4x-5)^2-2(16x^2-25)=0`
`<=>(4x-5)^2-2(4x-5)(4x+5)=0`
`<=>(4x-5)[(4x-5)-2(4x+5)]=0`
`<=>(4x-5)(4x-5-8x-10)=0`
`<=>(4x-5)(-4x-15)=0`
`<=>`\(\left[ \begin{array}{l}4x-5=0\\-4x-15=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=\dfrac54\\x=-\dfrac{15}4\end{array} \right.\)
Vậy `S={-15/4;5/4}`
d,
`(4x+3)^2=4(x^2-2x+1)`
`<=>(4x+3)^2=4(x-1)^2`
`<=>(4x+3)^2=[2(x-1)]^2`
`<=>(4x+3)^2=(2x-2)^2`
`<=>(4x+3)^2-(2x-2)^2=0`
`<=>(4x+3-2x+2)(4x+3+2x-2)=0`
`<=>(2x+5)(6x+1)=0`
`<=>`\(\left[ \begin{array}{l}2x+5=0\\6x+1=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=-\dfrac52\\x=-\dfrac16\end{array} \right.\)
Vậy `S={-5/2;-1/6}`
