Whakaoti i te c^2-c+3/2>0

$$c ^ { 2 } - c + \frac { 3 } { 2 } > 0$$

Whakaoti mō c

$$c\in \mathrm{R}$$

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.

$$c^{2}-c+\frac{3}{2}=0$$

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}{2} mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$c=\frac{1±\sqrt{-5}}{2}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā. He rite te tohu o te kīanga c^{2}-c+\frac{3}{2} ki tā tētahi c. Kia whakatau i te tohu, tātaitia te uara o te kīanga mō c=0.

$$0^{2}-0+\frac{3}{2}=\frac{3}{2}$$

Ko te uara o te kīanga c^{2}-c+\frac{3}{2} he tōrunga i ngā wā katoa. E mau ana te koreōrite mō c\in \mathrm{R}.

$$c\in \mathrm{R}$$