Whakaoti i te 8x^2+8x+(-1)leq0

$$8 x ^ { 2 } + 8 x + ( - 1 ) \leq 0$$

Whakaoti mō x

$$x\in \begin{bmatrix}-\frac{\sqrt{6}}{4}-\frac{1}{2},\frac{\sqrt{6}}{4}-\frac{1}{2}\end{bmatrix}$$

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.

$$8x^{2}+8x-1=0$$

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 8 mō te a, te 8 mō te b, me te -1 mō te c i te ture pūrua.

$$x=\frac{-8±\sqrt{8^{2}-4\times 8\left(-1\right)}}{2\times 8}$$

Mahia ngā tātaitai.

$$x=\frac{-8±4\sqrt{6}}{16}$$

Whakaotia te whārite x=\frac{-8±4\sqrt{6}}{16} ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{\sqrt{6}}{4}-\frac{1}{2} x=-\frac{\sqrt{6}}{4}-\frac{1}{2}$$

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

$$8\left(x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\right)\left(x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\right)\leq 0$$

Kia ≤0 te otinga, me ≥0 rawa tētahi uara o x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right) me x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right), me ≤0 anō te uara o tētahi. Whakaarohia te tauira ina ko x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\geq 0 me x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\leq 0.

$$x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\geq 0 x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\leq 0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina ko x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\leq 0 me x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\geq 0.

$$x-\left(-\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\geq 0 x-\left(\frac{\sqrt{6}}{4}-\frac{1}{2}\right)\leq 0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left[-\frac{\sqrt{6}}{4}-\frac{1}{2},\frac{\sqrt{6}}{4}-\frac{1}{2}\right].

$$x\in \begin{bmatrix}-\frac{\sqrt{6}}{4}-\frac{1}{2},\frac{\sqrt{6}}{4}-\frac{1}{2}\end{bmatrix}$$

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

$$x\in \begin{bmatrix}-\frac{\sqrt{6}}{4}-\frac{1}{2},\frac{\sqrt{6}}{4}-\frac{1}{2}\end{bmatrix}$$