Whakaoti i te x^2-4.06x+1.63^2=0

$${ x }^{ 2 } -4.06x+ { 1.63 }^{ 2 } =0$$

Whakaoti mō x

$$x=\frac{\sqrt{915}}{25}+2.03\approx 3.239958677$$

$$x=-\frac{\sqrt{915}}{25}+2.03\approx 0.820041323$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 1.63 mā te pū o 2, kia riro ko 2.6569.

$$x^{2}-4.06x+2.6569=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4.06 mō b, me 2.6569 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4.06\right)±\sqrt{\left(-4.06\right)^{2}-4\times 2.6569}}{2}$$

Pūruatia -4.06 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-4.06\right)±\sqrt{16.4836-4\times 2.6569}}{2}$$

Whakareatia -4 ki te 2.6569.

$$x=\frac{-\left(-4.06\right)±\sqrt{\frac{41209-26569}{2500}}}{2}$$

Tāpiri 16.4836 ki te -10.6276 mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-\left(-4.06\right)±\sqrt{5.856}}{2}$$

Tuhia te pūtakerua o te 5.856.

$$x=\frac{-\left(-4.06\right)±\frac{2\sqrt{915}}{25}}{2}$$

Ko te tauaro o -4.06 ko 4.06.

$$x=\frac{4.06±\frac{2\sqrt{915}}{25}}{2}$$

Nā, me whakaoti te whārite x=\frac{4.06±\frac{2\sqrt{915}}{25}}{2} ina he tāpiri te ±. Tāpiri 4.06 ki te \frac{2\sqrt{915}}{25}.

$$x=\frac{\frac{2\sqrt{915}}{25}+\frac{203}{50}}{2}$$

Whakawehe \frac{203}{50}+\frac{2\sqrt{915}}{25} ki te 2.

$$x=\frac{\sqrt{915}}{25}+\frac{203}{100}$$

Nā, me whakaoti te whārite x=\frac{4.06±\frac{2\sqrt{915}}{25}}{2} ina he tango te ±. Tango \frac{2\sqrt{915}}{25} mai i 4.06.

$$x=\frac{-\frac{2\sqrt{915}}{25}+\frac{203}{50}}{2}$$

Whakawehe \frac{203}{50}-\frac{2\sqrt{915}}{25} ki te 2.

$$x=-\frac{\sqrt{915}}{25}+\frac{203}{100}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{915}}{25}+\frac{203}{100} x=-\frac{\sqrt{915}}{25}+\frac{203}{100}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 1.63 mā te pū o 2, kia riro ko 2.6569.

$$x^{2}-4.06x+2.6569=0$$

Tangohia te 2.6569 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-4.06x=-2.6569$$

Whakawehea te -4.06, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2.03. Nā, tāpiria te pūrua o te -2.03 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-4.06x+\left(-2.03\right)^{2}=-2.6569+\left(-2.03\right)^{2}$$

Pūruatia -2.03 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-4.06x+4.1209=\frac{-26569+41209}{10000}$$

Tāpiri -2.6569 ki te 4.1209 mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-4.06x+4.1209=1.464$$

Tauwehea te x^{2}-4.06x+4.1209. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2.03\right)^{2}=1.464$$

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

$$\sqrt{\left(x-2.03\right)^{2}}=\sqrt{1.464}$$

Whakarūnātia.

$$x-2.03=\frac{\sqrt{915}}{25} x-2.03=-\frac{\sqrt{915}}{25}$$

Me tāpiri 2.03 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{915}}{25}+\frac{203}{100} x=-\frac{\sqrt{915}}{25}+\frac{203}{100}$$