Whakaoti i te x^2+4x-11<-36x-x^2

$$x ^ { 2 } + 4 x - 11 < - 36 x - x ^ { 2 }$$

Whakaoti mō x

$$x\in \left(-\frac{\sqrt{422}}{2}-10,\frac{\sqrt{422}}{2}-10\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 36x ki ngā taha e rua.

$$x^{2}+4x-11+36x<-x^{2}$$

Pahekotia te 4x me 36x, ka 40x.

$$x^{2}+40x-11<-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$x^{2}+40x-11+x^{2}<0$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}+40x-11<0$$

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.

$$2x^{2}+40x-11=0$$

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 40 mō te b, me te -11 mō te c i te ture pūrua.

$$x=\frac{-40±\sqrt{40^{2}-4\times 2\left(-11\right)}}{2\times 2}$$

Mahia ngā tātaitai.

$$x=\frac{-40±2\sqrt{422}}{4}$$

Whakaotia te whārite x=\frac{-40±2\sqrt{422}}{4} ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{\sqrt{422}}{2}-10 x=-\frac{\sqrt{422}}{2}-10$$

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

$$2\left(x-\left(\frac{\sqrt{422}}{2}-10\right)\right)\left(x-\left(-\frac{\sqrt{422}}{2}-10\right)\right)<0$$

Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-\left(\frac{\sqrt{422}}{2}-10\right) me te x-\left(-\frac{\sqrt{422}}{2}-10\right). Whakaarohia te tauira ina he tōrunga te x-\left(\frac{\sqrt{422}}{2}-10\right) he tōraro te x-\left(-\frac{\sqrt{422}}{2}-10\right).

$$x-\left(\frac{\sqrt{422}}{2}-10\right)>0 x-\left(-\frac{\sqrt{422}}{2}-10\right)<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te x-\left(-\frac{\sqrt{422}}{2}-10\right) he tōraro te x-\left(\frac{\sqrt{422}}{2}-10\right).

$$x-\left(-\frac{\sqrt{422}}{2}-10\right)>0 x-\left(\frac{\sqrt{422}}{2}-10\right)<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(-\frac{\sqrt{422}}{2}-10,\frac{\sqrt{422}}{2}-10\right).

$$x\in \left(-\frac{\sqrt{422}}{2}-10,\frac{\sqrt{422}}{2}-10\right)$$

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

$$x\in \left(-\frac{\sqrt{422}}{2}-10,\frac{\sqrt{422}}{2}-10\right)$$