Đáp án:
Giải thích các bước giải:
`6)`
`(2x-3)(x+2)-(4x-2)(x-5)=-16`
`⇔ 2x^2 + x - 6 - 4x^2 + 10x - 4 = -16`
`⇔ (2x^2-4x^2) + (x+10x) - (6+4) = -16`
`⇔ -2x^2 + 11x - 10 = -16`
`⇔ -2x^2 + 11x + 6 = 0`
`⇔ -(2x^2-11x-6) = 0`
`⇔ -[(2x^2+x)+(-12x-6)] = 0`
`⇔ -[x(2x+1)-6(2x+1)] = 0`
`⇔ -(2x+1)(x-6) = 0`
`⇔`\(\left[ \begin{array}{l}2x+1=0\\x-6=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-\dfrac12\\x=6\end{array} \right.\)
Vậy `S = {-1/2,6}`
`8)`
`(2x+1)(x-3) - 2x(x+7) = 100`
`⇔ 2x^2 - 5x - 3 - 2x^2 - 14x = 100`
`⇔ (2x^2-2x^2)-(14x+5x)-3 = 100`
`⇔ -19x - 3 = 100`
`⇔ -19x = 103`
`⇔ x = -103/19`
Vậy `S = {-103/19}`
`9)`
`(x+3)(x+1)-(x+4)(x+2)=8`
`⇔ x^2 + 4x + 3 - x^2 - 6x - 8 = 8`
`⇔ (x^2-x^2) - (6x-4x) - (8-3) = 8`
`⇔ -2x - 5 = 8`
`⇔ -2x = 13`
`⇔ x = -13/2`
Vậy `S = {-13/2}`
`13)`
`6(x-3)(x-1)-6(x^2+2)=36`
`⇔ 6x^2 - 24x + 18 - 6x^2 - 12 = 36`
`⇔ (6x^2-6x^2) - 24x + (18-12) = 36`
`⇔ -24x + 6 = 36`
`⇔ -24x = 30`
`⇔ x = -5/4`
Vậy `S = {-5/4}`
`14)`
`(3x-1)(x+2)-(2-3x)(x+3)=12`
`⇔ 3x^2 + 5x - 2 - (2-3x)(x+3) = 12`
`⇔ 3x^2 + 5x - 2 + 7x - 6 + 3x^2 = 12`
`⇔ (3x^2+3x^2) + (5x+7x) - (6+2) = 12`
`⇔ 6x^2 + 12x - 8 = 12`
`⇔ 6x^2 + 12x = 20`
`⇔ (6x^2+12x)/6 = 20/6`
`⇔ x^2 + 12/6x = 20/6`
`⇔ x^2 + 2x = 10/3`
`⇔ x^2 + 2x + 1^2 = 10/3 + 1^2`
`⇔ x^2 + 2x + 1 = 13/3`
`⇔ x^2 + 2x * 1 + 1^2 = 13/3`
`⇔ (x+1)^2 = 13/3`
`⇔ |x+1| = sqrt{39}/3`
`⇔`\(\left[ \begin{array}{l}x+1=\dfrac{\sqrt{39}}3\\x+1=-\dfrac{\sqrt{39}}3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{\sqrt{39}}3-1\\x=-\dfrac{\sqrt{39}}3-1\end{array} \right.\)
Vậy `S = {sqrt{39}/3-1,-sqrt{39}/3-1}`
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Câu `14)` áp dụng hằng đẳng thức :
`a^2 + 2ab + b^2 = (a+b)^2`
