Tìm x,biết: a)$(x-2)^{2}$ -(x-3)(x+3)=6 b)2(x+3)-$x^{2}$ -3x=0 02/12/2021 Bởi Amara Tìm x,biết: a)$(x-2)^{2}$ -(x-3)(x+3)=6 b)2(x+3)-$x^{2}$ -3x=0
`\text{~~Holi~~}` `a. (x-2)^2-(x-3)(x+3)=6` `-> x^2-4x-4-x^2+9=6` `-> -4x+13=6` `-> -4x=6-13` `-> -4x=-7` `-> x=(-7)/(-4)` `-> x=7/4` `b. 2(x+3)-x^2-3x=0` `-> -2(x+3)+x^2+3x=0` `-> -(x+3)(2-x)=0` `-> (x+3)(2-x)=0` `->` \(\left[ \begin{array}{l}x+3=0\\2-x=0\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=-3\\x=2\end{array} \right.\) Bình luận
Đáp án: `a) x= \frac{7}{4}` `b)` $\left \{ {{x=-3} \atop {x=2}} \right.$ Giải thích các bước giải: `a) (x – 2)^2 – (x – 3)(x + 3) = 6` `=> x^2 – 2.x.2 + 2^2 – (x^2 – 9) = 6` `=> x^2 – 4x + 4 – x^2 + 9 = 6` `=> -4x + 4 + 9 = 6 => -4x = -7=> x = \frac{7}{4}` `b) 2(x + 3) – x^2 – 3x = 0` `=> 2(x + 3) – (x^2 + 3x) = 0` `=> 2(x + 3) – x(x + 3) = 0` `=> (x + 3)(2 – x) = 0` `=>` $\left \{ {{x + 3 = 0} \atop {2 – x = 0}} \right.$ `=>` $\left \{ {{x=-3} \atop {x=2}} \right.$ Bình luận
`\text{~~Holi~~}`
`a. (x-2)^2-(x-3)(x+3)=6`
`-> x^2-4x-4-x^2+9=6`
`-> -4x+13=6`
`-> -4x=6-13`
`-> -4x=-7`
`-> x=(-7)/(-4)`
`-> x=7/4`
`b. 2(x+3)-x^2-3x=0`
`-> -2(x+3)+x^2+3x=0`
`-> -(x+3)(2-x)=0`
`-> (x+3)(2-x)=0`
`->` \(\left[ \begin{array}{l}x+3=0\\2-x=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=-3\\x=2\end{array} \right.\)
Đáp án:
`a) x= \frac{7}{4}`
`b)` $\left \{ {{x=-3} \atop {x=2}} \right.$
Giải thích các bước giải:
`a) (x – 2)^2 – (x – 3)(x + 3) = 6`
`=> x^2 – 2.x.2 + 2^2 – (x^2 – 9) = 6`
`=> x^2 – 4x + 4 – x^2 + 9 = 6`
`=> -4x + 4 + 9 = 6 => -4x = -7=> x = \frac{7}{4}`
`b) 2(x + 3) – x^2 – 3x = 0`
`=> 2(x + 3) – (x^2 + 3x) = 0`
`=> 2(x + 3) – x(x + 3) = 0`
`=> (x + 3)(2 – x) = 0`
`=>` $\left \{ {{x + 3 = 0} \atop {2 – x = 0}} \right.$
`=>` $\left \{ {{x=-3} \atop {x=2}} \right.$