Whakaoti i te 6x^2+33x+36leq0

$$6 x ^ { 2 } + 33 x + 36 \leq 0$$

Whakaoti mō x

$$x\in \begin{bmatrix}-4,-\frac{3}{2}\end{bmatrix}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$6x^{2}+33x+36=0$$

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 6 mō te a, te 33 mō te b, me te 36 mō te c i te ture pūrua.

$$x=\frac{-33±\sqrt{33^{2}-4\times 6\times 36}}{2\times 6}$$

Mahia ngā tātaitai.

$$x=\frac{-33±15}{12}$$

Whakaotia te whārite x=\frac{-33±15}{12} ina he tōrunga te ±, ina he tōraro te ±.

$$x=-\frac{3}{2} x=-4$$

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

$$6\left(x+\frac{3}{2}\right)\left(x+4\right)\leq 0$$

Kia ≤0 te otinga, me ≥0 rawa tētahi uara o x+\frac{3}{2} me x+4, me ≤0 anō te uara o tētahi. Whakaarohia te tauira ina ko x+\frac{3}{2}\geq 0 me x+4\leq 0.

$$x+\frac{3}{2}\geq 0 x+4\leq 0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina ko x+\frac{3}{2}\leq 0 me x+4\geq 0.

$$x+4\geq 0 x+\frac{3}{2}\leq 0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left[-4,-\frac{3}{2}\right].

$$x\in \begin{bmatrix}-4,-\frac{3}{2}\end{bmatrix}$$

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

$$x\in \begin{bmatrix}-4,-\frac{3}{2}\end{bmatrix}$$