Whakaoti i te 8y^3-27=0

$$8 y ^ { 3 } - 27 = 0$$

Whakaoti mō y

$$y = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -27, ā, ka wehea e q te whakarea arahanga 8. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{27}{8},±\frac{27}{4},±\frac{27}{2},±27,±\frac{9}{8},±\frac{9}{4},±\frac{9}{2},±9,±\frac{3}{8},±\frac{3}{4},±\frac{3}{2},±3,±\frac{1}{8},±\frac{1}{4},±\frac{1}{2},±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$y=\frac{3}{2}$$

Mā te whakatakotoranga Tauwehe, he tauwehe te y-k o te pūrau mō ia pūtake k. Whakawehea te 8y^{3}-27 ki te 2\left(y-\frac{3}{2}\right)=2y-3, kia riro ko 4y^{2}+6y+9. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$4y^{2}+6y+9=0$$

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 4 mō te a, te 6 mō te b, me te 9 mō te c i te ture pūrua.

$$y=\frac{-6±\sqrt{6^{2}-4\times 4\times 9}}{2\times 4}$$

Mahia ngā tātaitai.

$$y=\frac{-6±\sqrt{-108}}{8}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$y\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$y=\frac{3}{2}$$