Whakaoti i te {l}{a+b=6}{a^2+b^2=6}

$$\left. \begin{array} { l } { a + b = 6 } \\ { a ^ { 2 } + b ^ { 2 } = 6 } \end{array} \right.$$

Whakaoti mō a, b

$$a=3+\sqrt{6}i\approx 3+2.449489743i\text{, }b=-\sqrt{6}i+3\approx 3-2.449489743i$$

$$a=-\sqrt{6}i+3\approx 3-2.449489743i\text{, }b=3+\sqrt{6}i\approx 3+2.449489743i$$

Ngā Upane e Whakamahi ana i te Whakakapinga me te Tikanga Tātai Pūrua

Whakaotia te a+b=6 mō a mā te wehe i te a i te taha mauī o te tohu ōrite.

$$a+b=6$$

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

$$a=-b+6$$

Whakakapia te -b+6 mō te a ki tērā atu whārite, b^{2}+a^{2}=6.

$$b^{2}+\left(-b+6\right)^{2}=6$$

Pūrua -b+6.

$$b^{2}+b^{2}-12b+36=6$$

Tāpiri b^{2} ki te b^{2}.

$$2b^{2}-12b+36=6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$2b^{2}-12b+30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\left(-1\right)^{2} mō a, 1\times 6\left(-1\right)\times 2 mō b, me 30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 2\times 30}}{2\times 2}$$

Pūrua 1\times 6\left(-1\right)\times 2.

$$b=\frac{-\left(-12\right)±\sqrt{144-4\times 2\times 30}}{2\times 2}$$

Whakareatia -4 ki te 1+1\left(-1\right)^{2}.

$$b=\frac{-\left(-12\right)±\sqrt{144-8\times 30}}{2\times 2}$$

Whakareatia -8 ki te 30.

$$b=\frac{-\left(-12\right)±\sqrt{144-240}}{2\times 2}$$

Tāpiri 144 ki te -240.

$$b=\frac{-\left(-12\right)±\sqrt{-96}}{2\times 2}$$

Tuhia te pūtakerua o te -96.

$$b=\frac{-\left(-12\right)±4\sqrt{6}i}{2\times 2}$$

Ko te tauaro o 1\times 6\left(-1\right)\times 2 ko 12.

$$b=\frac{12±4\sqrt{6}i}{2\times 2}$$

Whakareatia 2 ki te 1+1\left(-1\right)^{2}.

$$b=\frac{12±4\sqrt{6}i}{4}$$

Nā, me whakaoti te whārite b=\frac{12±4\sqrt{6}i}{4} ina he tāpiri te ±. Tāpiri 12 ki te 4i\sqrt{6}.

$$b=\frac{12+4\sqrt{6}i}{4}$$

Whakawehe 12+4i\sqrt{6} ki te 4.

$$b=3+\sqrt{6}i$$

Nā, me whakaoti te whārite b=\frac{12±4\sqrt{6}i}{4} ina he tango te ±. Tango 4i\sqrt{6} mai i 12.

$$b=\frac{-4\sqrt{6}i+12}{4}$$

Whakawehe 12-4i\sqrt{6} ki te 4.

$$b=-\sqrt{6}i+3$$

E rua ngā otinga mō b: 3+i\sqrt{6} me 3-i\sqrt{6}. Me whakakapi 3+i\sqrt{6} mō b ki te whārite a=-b+6 hei kimi i te otinga hāngai mō a e pai ai ki ngā whārite e rua.

$$a=-\left(3+\sqrt{6}i\right)+6$$

Me whakakapi te 3-i\sqrt{6} ināianei mō te b ki te whārite a=-b+6 ka whakaoti hei kimi i te otinga hāngai mō a e pai ai ki ngā whārite e rua.

$$a=-\left(-\sqrt{6}i+3\right)+6$$

Kua oti te pūnaha te whakatau.

$$a=-\left(3+\sqrt{6}i\right)+6,b=3+\sqrt{6}i\text{ or }a=-\left(-\sqrt{6}i+3\right)+6,b=-\sqrt{6}i+3$$