Whakaoti i te x^2+2x-3<0

$${ x }^{ 2 } +2x-3 < 0$$

Whakaoti mō x

$$x\in \left(-3,1\right)$$

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.

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

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 2 mō te b, me te -3 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-2±4}{2}$$

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

$$x=1 x=-3$$

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

$$\left(x-1\right)\left(x+3\right)<0$$

Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-1 me te x+3. Whakaarohia te tauira ina he tōrunga te x-1 he tōraro te x+3.

$$x-1>0 x+3<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te x+3 he tōraro te x-1.

$$x+3>0 x-1<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(-3,1\right).

$$x\in \left(-3,1\right)$$

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

$$x\in \left(-3,1\right)$$