Whakaoti i te 3x^2+2x-5>0

$$3 x ^ { 2 } + 2 x - 5 > 0$$

Whakaoti mō x

$$x\in \left(-\infty,-\frac{5}{3}\right)\cup \left(1,\infty\right)$$

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.

$$3x^{2}+2x-5=0$$

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 3 mō te a, te 2 mō te b, me te -5 mō te c i te ture pūrua.

$$x=\frac{-2±\sqrt{2^{2}-4\times 3\left(-5\right)}}{2\times 3}$$

Mahia ngā tātaitai.

$$x=\frac{-2±8}{6}$$

Whakaotia te whārite x=\frac{-2±8}{6} ina he tōrunga te ±, ina he tōraro te ±.

$$x=1 x=-\frac{5}{3}$$

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

$$3\left(x-1\right)\left(x+\frac{5}{3}\right)>0$$

Kia tōrunga te otinga, me tōraro tahi te x-1 me te x+\frac{5}{3}, me tōrunga tahi rānei. Whakaarohia te tauira ina he tōraro tahi te x-1 me te x+\frac{5}{3}.

$$x-1<0 x+\frac{5}{3}<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x<-\frac{5}{3}.

$$x<-\frac{5}{3}$$

Whakaarohia te tauira ina he tōrunga tahi te x-1 me te x+\frac{5}{3}.

$$x+\frac{5}{3}>0 x-1>0$$

Te otinga e whakaea i ngā koreōrite e rua ko x>1.

$$x>1$$

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

$$x<-\frac{5}{3}\text{; }x>1$$