Whakaoti i te 6-x^2+4x-3geq0

$$6 - x ^ { 2 } + 4 x - 3 \geq 0$$

Whakaoti mō x

$$x\in \begin{bmatrix}2-\sqrt{7},\sqrt{7}+2\end{bmatrix}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 3 i te 6, ka 3.

$$3-x^{2}+4x\geq 0$$

Me whakarea te koreōrite ki te -1 kia tōrunga ai te tau whakarea o te pū tino teitei i 3-x^{2}+4x. I te mea he tōraro a -1, ka huri te ahunga koreōrite.

$$-3+x^{2}-4x\leq 0$$

Kia whakaotia te koreōrite, me tauwehe te taha mauī. Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$-3+x^{2}-4x=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te -4 mō te b, me te -3 mō te c i te ture pūrua.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\left(-3\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{4±2\sqrt{7}}{2}$$

Whakaotia te whārite x=\frac{4±2\sqrt{7}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$x=\sqrt{7}+2 x=2-\sqrt{7}$$

Tuhia anō te koreōrite mā te whakamahi i ngā otinga i whiwhi.

$$\left(x-\left(\sqrt{7}+2\right)\right)\left(x-\left(2-\sqrt{7}\right)\right)\leq 0$$

Kia ≤0 te otinga, me ≥0 rawa tētahi uara o x-\left(\sqrt{7}+2\right) me x-\left(2-\sqrt{7}\right), me ≤0 anō te uara o tētahi. Whakaarohia te tauira ina ko x-\left(\sqrt{7}+2\right)\geq 0 me x-\left(2-\sqrt{7}\right)\leq 0.

$$x-\left(\sqrt{7}+2\right)\geq 0 x-\left(2-\sqrt{7}\right)\leq 0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina ko x-\left(\sqrt{7}+2\right)\leq 0 me x-\left(2-\sqrt{7}\right)\geq 0.

$$x-\left(2-\sqrt{7}\right)\geq 0 x-\left(\sqrt{7}+2\right)\leq 0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left[2-\sqrt{7},\sqrt{7}+2\right].

$$x\in \begin{bmatrix}2-\sqrt{7},\sqrt{7}+2\end{bmatrix}$$

Ko te otinga whakamutunga ko te whakakotahi i ngā otinga kua whiwhi.

$$x\in \begin{bmatrix}2-\sqrt{7},\sqrt{7}+2\end{bmatrix}$$