Phân tích thành nhân tử : 3x^2 + 3x-1 = 0 25/09/2021 Bởi Iris Phân tích thành nhân tử : 3x^2 + 3x-1 = 0
$3x^2+3x-1=0$ $\to (\sqrt3 x)^2+2.\sqrt3 x.\dfrac{\sqrt3}{2}+\Big(\dfrac{\sqrt3}{2}\Big)^2-\dfrac{7}{4}=0$ $\to \Big(\sqrt3 x+\dfrac{\sqrt3}{2}\Big)^2-\Big(\dfrac{\sqrt7}{2}\Big)^2=0$ $\to \Big(\sqrt3 x+\dfrac{\sqrt3-\sqrt7}{2}\Big).\Big(\sqrt3 x+\dfrac{\sqrt3+\sqrt7}{2}\Big)=0$ Bình luận
Đáp án: Giải thích các bước giải: `3x^2+3x-1=0` `<=>x^2+x-1/3=0` `<=>x^2+x+1/4-7/12=0` `<=>(x+1/2)^2-7/12=0` `<=>(x+1/2)^2=7/12` `<=>x+1/2=+-sqrt(7/12)` `<=>`\(\left[ \begin{array}{l}x+\dfrac{1}{2}=\sqrt{\dfrac{7}{12}}\\x+\dfrac{1}{2}=-\sqrt{\dfrac{7}{12}}\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=\sqrt{\dfrac{7}{12}}-\dfrac{1}{2}\\x=-\sqrt{\dfrac{7}{12}}-\dfrac{1}{2}\end{array} \right.\) Bình luận
$3x^2+3x-1=0$
$\to (\sqrt3 x)^2+2.\sqrt3 x.\dfrac{\sqrt3}{2}+\Big(\dfrac{\sqrt3}{2}\Big)^2-\dfrac{7}{4}=0$
$\to \Big(\sqrt3 x+\dfrac{\sqrt3}{2}\Big)^2-\Big(\dfrac{\sqrt7}{2}\Big)^2=0$
$\to \Big(\sqrt3 x+\dfrac{\sqrt3-\sqrt7}{2}\Big).\Big(\sqrt3 x+\dfrac{\sqrt3+\sqrt7}{2}\Big)=0$
Đáp án:
Giải thích các bước giải:
`3x^2+3x-1=0`
`<=>x^2+x-1/3=0`
`<=>x^2+x+1/4-7/12=0`
`<=>(x+1/2)^2-7/12=0`
`<=>(x+1/2)^2=7/12`
`<=>x+1/2=+-sqrt(7/12)`
`<=>`\(\left[ \begin{array}{l}x+\dfrac{1}{2}=\sqrt{\dfrac{7}{12}}\\x+\dfrac{1}{2}=-\sqrt{\dfrac{7}{12}}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\sqrt{\dfrac{7}{12}}-\dfrac{1}{2}\\x=-\sqrt{\dfrac{7}{12}}-\dfrac{1}{2}\end{array} \right.\)