Whakaoti i te 1+x^2-21x=050565

$$1 + x ^ { 2 } - 21 x = 050565$$

Whakaoti mō x

$$x = \frac{\sqrt{437} + 21}{2} \approx 20.95227248$$

$$x=\frac{21-\sqrt{437}}{2}\approx 0.04772752$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 50565, ka 0.

$$1+x^{2}-21x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-21x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -21 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4}}{2}$$

Pūrua -21.

$$x=\frac{-\left(-21\right)±\sqrt{441-4}}{2}$$

Tāpiri 441 ki te -4.

$$x=\frac{-\left(-21\right)±\sqrt{437}}{2}$$

Ko te tauaro o -21 ko 21.

$$x=\frac{21±\sqrt{437}}{2}$$

Nā, me whakaoti te whārite x=\frac{21±\sqrt{437}}{2} ina he tāpiri te ±. Tāpiri 21 ki te \sqrt{437}.

$$x=\frac{\sqrt{437}+21}{2}$$

Nā, me whakaoti te whārite x=\frac{21±\sqrt{437}}{2} ina he tango te ±. Tango \sqrt{437} mai i 21.

$$x=\frac{21-\sqrt{437}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{437}+21}{2} x=\frac{21-\sqrt{437}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 50565, ka 0.

$$1+x^{2}-21x=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-21x=-1$$

Whakawehea te -21, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{21}{2}. Nā, tāpiria te pūrua o te -\frac{21}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-21x+\left(-\frac{21}{2}\right)^{2}=-1+\left(-\frac{21}{2}\right)^{2}$$

Pūruatia -\frac{21}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-21x+\frac{441}{4}=-1+\frac{441}{4}$$

Tāpiri -1 ki te \frac{441}{4}.

$$x^{2}-21x+\frac{441}{4}=\frac{437}{4}$$

Tauwehea x^{2}-21x+\frac{441}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{21}{2}\right)^{2}=\frac{437}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{21}{2}\right)^{2}}=\sqrt{\frac{437}{4}}$$

Whakarūnātia.

$$x-\frac{21}{2}=\frac{\sqrt{437}}{2} x-\frac{21}{2}=-\frac{\sqrt{437}}{2}$$

Me tāpiri \frac{21}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{437}+21}{2} x=\frac{21-\sqrt{437}}{2}$$