Whakaoti i te 6x^2-162x+840<0

$$6 { x }^{ 2 } -162x+840 < 0$$

Whakaoti mō x

$$x\in \left(7,20\right)$$

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.

$$6x^{2}-162x+840=0$$

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 6 mō te a, te -162 mō te b, me te 840 mō te c i te ture pūrua.

$$x=\frac{-\left(-162\right)±\sqrt{\left(-162\right)^{2}-4\times 6\times 840}}{2\times 6}$$

Mahia ngā tātaitai.

$$x=\frac{162±78}{12}$$

Whakaotia te whārite x=\frac{162±78}{12} ina he tōrunga te ±, ina he tōraro te ±.

$$x=20 x=7$$

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

$$6\left(x-20\right)\left(x-7\right)<0$$

Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-20 me te x-7. Whakaarohia te tauira ina he tōrunga te x-20 he tōraro te x-7.

$$x-20>0 x-7<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te x-7 he tōraro te x-20.

$$x-7>0 x-20<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(7,20\right).

$$x\in \left(7,20\right)$$

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

$$x\in \left(7,20\right)$$