Đáp án + Giải thích các bước giải:
`a//(2x+5)^{2}=(3x-1)^{2}`
`⇔(2x+5)^{2}-(3x-1)^{2}=0`
`⇔(2x+5+3x-1)(2x+5-3x+1)=0`
`⇔(5x+4)(-x+6)=0`
`⇔` \(\left[ \begin{array}{l}5x+4=0\\-x+6=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-\frac{4}{5}\\x=6\end{array} \right.\)
Vậy `S={-\frac{4}{5};6}`
`b//4x^{2}(x-1)-x+1=0`
`⇔4x^{2}(x-1)-(x-1)=0`
`⇔(x-1)(4x^{2}-1)=0`
`⇔(x-1)(2x-1)(2x+1)=0`
`⇔` \(\left[ \begin{array}{l}x-1=0\\2x-1=0\\2x+1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=1\\x=\frac{1}{2}\\x=-\frac{1}{2}\end{array} \right.\)
Vậy `S={1;\frac{1}{2};-\frac{1}{2}}`
`c//9(2x+1)^{2}=4(x-5)^{2}`
`⇔9(4x^{2}+4x+1)=4(x^{2}-10x+25)`
`⇔36x^{2}+36x+9=4x^{2}-40x+100`
`⇔36x^{2}-4x^{2}+36x+40x+9-100=0`
`⇔32x^{2}+76x-91=0`
`⇔32(x^{2}+(19)/(8)x-(91)/(32))=0`
`⇔x^{2}+(19)/(8)x-(91)/(32)=0`
`⇔x^{2}+2.x.(19)/(16)+((19)/(16))^{2}-(1089)/(256)=0`
`⇔(x+(19)/(16))^{2}=(1089)/(256)`
`⇔x+(19)/(16)=±(33)/(16)`
`⇔` \(\left[ \begin{array}{l}x=\frac{7}{8}\\x=-\frac{13}{4}\end{array} \right.\)
Vậy `S={\frac{7}{8};-\frac{13}{4}}`
