Whakaoti i te AA+2A=65

$$A A + 2 A = 65$$

Whakaoti mō A

$$A=\sqrt{66}-1\approx 7.124038405$$

$$A=-\sqrt{66}-1\approx -9.124038405$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te A ki te A, ka A^{2}.

$$A^{2}+2A=65$$

Tangohia te 65 mai i ngā taha e rua.

$$A^{2}+2A-65=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -65 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{-2±\sqrt{2^{2}-4\left(-65\right)}}{2}$$

Pūrua 2.

$$A=\frac{-2±\sqrt{4-4\left(-65\right)}}{2}$$

Whakareatia -4 ki te -65.

$$A=\frac{-2±\sqrt{4+260}}{2}$$

Tāpiri 4 ki te 260.

$$A=\frac{-2±\sqrt{264}}{2}$$

Tuhia te pūtakerua o te 264.

$$A=\frac{-2±2\sqrt{66}}{2}$$

Nā, me whakaoti te whārite A=\frac{-2±2\sqrt{66}}{2} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{66}.

$$A=\frac{2\sqrt{66}-2}{2}$$

Whakawehe -2+2\sqrt{66} ki te 2.

$$A=\sqrt{66}-1$$

Nā, me whakaoti te whārite A=\frac{-2±2\sqrt{66}}{2} ina he tango te ±. Tango 2\sqrt{66} mai i -2.

$$A=\frac{-2\sqrt{66}-2}{2}$$

Whakawehe -2-2\sqrt{66} ki te 2.

$$A=-\sqrt{66}-1$$

Kua oti te whārite te whakatau.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te A ki te A, ka A^{2}.

$$A^{2}+2A=65$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$A^{2}+2A+1^{2}=65+1^{2}$$

Pūrua 1.

$$A^{2}+2A+1=65+1$$

Tāpiri 65 ki te 1.

$$A^{2}+2A+1=66$$

Tauwehea A^{2}+2A+1. 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}.

$$\left(A+1\right)^{2}=66$$

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

$$\sqrt{\left(A+1\right)^{2}}=\sqrt{66}$$

Whakarūnātia.

$$A+1=\sqrt{66} A+1=-\sqrt{66}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$