Whakaoti i te m^2-m-3/4geq0

$$m ^ { 2 } - m - \frac { 3 } { 4 } \geq 0$$

Whakaoti mō m

$$m\in (-\infty,-\frac{1}{2}]\cup [\frac{3}{2},\infty)$$

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.

$$m^{2}-m-\frac{3}{4}=0$$

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 1 mō te a, te -1 mō te b, me te -\frac{3}{4} mō te c i te ture pūrua.

$$m=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-\frac{3}{4}\right)}}{2}$$

Mahia ngā tātaitai.

$$m=\frac{1±2}{2}$$

Whakaotia te whārite m=\frac{1±2}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$m=\frac{3}{2} m=-\frac{1}{2}$$

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

$$\left(m-\frac{3}{2}\right)\left(m+\frac{1}{2}\right)\geq 0$$

Kia ≥0 te otinga, me ≤0 tahi, me ≥0 tahi rānei te m-\frac{3}{2} me te m+\frac{1}{2}. Whakaarohia te tauira ina he ≤0 tahi te m-\frac{3}{2} me te m+\frac{1}{2}.

$$m-\frac{3}{2}\leq 0 m+\frac{1}{2}\leq 0$$

Te otinga e whakaea i ngā koreōrite e rua ko m\leq -\frac{1}{2}.

$$m\leq -\frac{1}{2}$$

Whakaarohia te tauira ina he ≥0 tahi te m-\frac{3}{2} me te m+\frac{1}{2}.

$$m+\frac{1}{2}\geq 0 m-\frac{3}{2}\geq 0$$

Te otinga e whakaea i ngā koreōrite e rua ko m\geq \frac{3}{2}.

$$m\geq \frac{3}{2}$$

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

$$m\leq -\frac{1}{2}\text{; }m\geq \frac{3}{2}$$