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Whakaoti mō x
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2x^{2}-x-3-\left(x-2\right)<0
Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te x+1 ka whakakotahi i ngā kupu rite.
2x^{2}-x-3-x+2<0
Hei kimi i te tauaro o x-2, kimihia te tauaro o ia taurangi.
2x^{2}-2x-3+2<0
Pahekotia te -x me -x, ka -2x.
2x^{2}-2x-1<0
Tāpirihia te -3 ki te 2, ka -1.
2x^{2}-2x-1=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.
x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\left(-1\right)}}{2\times 2}
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 -2 mō te b, me te -1 mō te c i te ture pūrua.
x=\frac{2±2\sqrt{3}}{4}
Mahia ngā tātaitai.
x=\frac{\sqrt{3}+1}{2} x=\frac{1-\sqrt{3}}{2}
Whakaotia te whārite x=\frac{2±2\sqrt{3}}{4} ina he tōrunga te ±, ina he tōraro te ±.
2\left(x-\frac{\sqrt{3}+1}{2}\right)\left(x-\frac{1-\sqrt{3}}{2}\right)<0
Tuhia anō te koreōrite mā te whakamahi i ngā otinga i whiwhi.
x-\frac{\sqrt{3}+1}{2}>0 x-\frac{1-\sqrt{3}}{2}<0
Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-\frac{\sqrt{3}+1}{2} me te x-\frac{1-\sqrt{3}}{2}. Whakaarohia te tauira ina he tōrunga te x-\frac{\sqrt{3}+1}{2} he tōraro te x-\frac{1-\sqrt{3}}{2}.
x\in \emptyset
He teka tēnei mō tētahi x ahakoa.
x-\frac{1-\sqrt{3}}{2}>0 x-\frac{\sqrt{3}+1}{2}<0
Whakaarohia te tauira ina he tōrunga te x-\frac{1-\sqrt{3}}{2} he tōraro te x-\frac{\sqrt{3}+1}{2}.
x\in \left(\frac{1-\sqrt{3}}{2},\frac{\sqrt{3}+1}{2}\right)
Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(\frac{1-\sqrt{3}}{2},\frac{\sqrt{3}+1}{2}\right).
x\in \left(\frac{1-\sqrt{3}}{2},\frac{\sqrt{3}+1}{2}\right)
Ko te otinga whakamutunga ko te whakakotahi i ngā otinga kua whiwhi.