Đáp án:
Bài `46:`
`1)x∈{-1/2;2}`
`2)x∈{10/3;-1}`
`3)x∈{1;3/2}`
Bài `47:`
`1)x∈{8;3}`
`2)x∈{6;-2}`
Giải thích các bước giải:
Bài `46:`
`1)2x^2-3x-2=0`
`⇔2x^2-4x+x-2=0`
`⇔(2x^2-4x)+(x-2)=0`
`⇔2x(x-2)+(x-2)=0`
`⇔(2x+1)(x-2)=0`
`⇔`\(\left[ \begin{array}{l}2x+1=0\\x-2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{-1}{2}\\x=2\end{array} \right.\)
Vậy `x∈{-1/2;2}`
`2)3x^2-7x-10=0`
`⇔3x^2-10x+3x-10=0`
`⇔(3x^2-10x)+(3x-10)=0`
`⇔x(3x-10)+(3x-10)=0`
`⇔(3x-10)(x+1)=0`
`⇔`\(\left[ \begin{array}{l}3x-10=0\\x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}3x=10\\x=-1\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{10}{3}\\x=-1\end{array} \right.\)
Vậy `x∈{10/3;-1}`
`3)2x^2-5x+3=0`
`⇔2x^2-2x-3x+3=0`
`⇔(2x^2-2x)-(3x-3)=0`
`⇔2x(x-1)-3(x-1)=0`
`⇔(x-1)(2x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-1=0\\2x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1\\2x=3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1\\x=\dfrac{3}{2}\end{array} \right.\)
Vậy `x∈{1;3/2}`
Bài `47:`
`1)(x-3)^2-5(x-2)+5=0`
`⇔x^2-6x+9-5x+10+5=0`
`⇔x^2+(-6x-5x)+(9+10+5)=0`
`⇔x^2-11x+24=0`
`⇔x^2-8x-3x+24=0`
`⇔(x^2-8x)-(3x-24)=0`
`⇔x(x-8)-3(x-8)=0`
`⇔(x-8)(x-3)=0`
`⇔`\(\left[ \begin{array}{l}x-8=0\\x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=8\\x=3\end{array} \right.\)
Vậy `x∈{8;3}`
`2)(2x-1)^2-3(x-2)(x+2)-25=0`
`⇔(2x)^2-2.2x.1+1-3(x^2-4)-25=0`
`⇔4x^2-4x+1-3x^2+12-25=0`
`⇔(4x^2-3x^2)-4x+(1+12-25)=0`
`⇔x^2-4x-12=0`
`⇔x^2-6x+2x-12=0`
`⇔(x^2-6x)+(2x-12)=0`
`⇔x(x-6)+2(x-6)=0`
`⇔(x-6)(x+2)=0`
`⇔`\(\left[ \begin{array}{l}x-6=0\\x+2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=6\\x=-2\end{array} \right.\)
Vậy `x∈{6;-2}`
