Whakaoti i te x^2+2x-15>0

$$x ^ { 2 } + 2 x - 15 > 0$$

Whakaoti mō x

$$x\in \left(-\infty,-5\right)\cup \left(3,\infty\right)$$

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.

$$x^{2}+2x-15=0$$

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 -15 mō te c i te ture pūrua.

$$x=\frac{-2±\sqrt{2^{2}-4\times 1\left(-15\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-2±8}{2}$$

Whakaotia te whārite x=\frac{-2±8}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$x=3 x=-5$$

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

$$\left(x-3\right)\left(x+5\right)>0$$

Kia tōrunga te otinga, me tōraro tahi te x-3 me te x+5, me tōrunga tahi rānei. Whakaarohia te tauira ina he tōraro tahi te x-3 me te x+5.

$$x-3<0 x+5<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x<-5.

$$x<-5$$

Whakaarohia te tauira ina he tōrunga tahi te x-3 me te x+5.

$$x+5>0 x-3>0$$

Te otinga e whakaea i ngā koreōrite e rua ko x>3.

$$x>3$$

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

$$x<-5\text{; }x>3$$