Whakaoti i te 53x^2+5x-12<0

$$53 x ^ { 2 } + 5 x - 12 < 0$$

Whakaoti mō x

$$x\in \left(\frac{-\sqrt{2569}-5}{106},\frac{\sqrt{2569}-5}{106}\right)$$

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.

$$53x^{2}+5x-12=0$$

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 53 mō te a, te 5 mō te b, me te -12 mō te c i te ture pūrua.

$$x=\frac{-5±\sqrt{5^{2}-4\times 53\left(-12\right)}}{2\times 53}$$

Mahia ngā tātaitai.

$$x=\frac{-5±\sqrt{2569}}{106}$$

Whakaotia te whārite x=\frac{-5±\sqrt{2569}}{106} ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{\sqrt{2569}-5}{106} x=\frac{-\sqrt{2569}-5}{106}$$

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

$$53\left(x-\frac{\sqrt{2569}-5}{106}\right)\left(x-\frac{-\sqrt{2569}-5}{106}\right)<0$$

Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-\frac{\sqrt{2569}-5}{106} me te x-\frac{-\sqrt{2569}-5}{106}. Whakaarohia te tauira ina he tōrunga te x-\frac{\sqrt{2569}-5}{106} he tōraro te x-\frac{-\sqrt{2569}-5}{106}.

$$x-\frac{\sqrt{2569}-5}{106}>0 x-\frac{-\sqrt{2569}-5}{106}<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te x-\frac{-\sqrt{2569}-5}{106} he tōraro te x-\frac{\sqrt{2569}-5}{106}.

$$x-\frac{-\sqrt{2569}-5}{106}>0 x-\frac{\sqrt{2569}-5}{106}<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(\frac{-\sqrt{2569}-5}{106},\frac{\sqrt{2569}-5}{106}\right).

$$x\in \left(\frac{-\sqrt{2569}-5}{106},\frac{\sqrt{2569}-5}{106}\right)$$

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

$$x\in \left(\frac{-\sqrt{2569}-5}{106},\frac{\sqrt{2569}-5}{106}\right)$$