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

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

Whakaoti mō x

$$x\in \left(-\infty,-3\right)\cup \left(\frac{1}{2},\infty\right)$$

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.

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

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

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

Mahia ngā tātaitai.

$$x=\frac{-5±7}{4}$$

Whakaotia te whārite x=\frac{-5±7}{4} ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{1}{2} x=-3$$

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

$$2\left(x-\frac{1}{2}\right)\left(x+3\right)>0$$

Kia tōrunga te otinga, me tōraro tahi te x-\frac{1}{2} me te x+3, me tōrunga tahi rānei. Whakaarohia te tauira ina he tōraro tahi te x-\frac{1}{2} me te x+3.

$$x-\frac{1}{2}<0 x+3<0$$

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

$$x<-3$$

Whakaarohia te tauira ina he tōrunga tahi te x-\frac{1}{2} me te x+3.

$$x+3>0 x-\frac{1}{2}>0$$

Te otinga e whakaea i ngā koreōrite e rua ko x>\frac{1}{2}.

$$x>\frac{1}{2}$$

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

$$x<-3\text{; }x>\frac{1}{2}$$