Whakaoti i te {l}{a^2+b^2=13}{a+b=4}

$$\left. \begin{array} { l } { a ^ { 2 } + b ^ { 2 } = 13 } \\ { a + b = 4 } \end{array} \right.$$

Whakaoti mō a, b

$$a=\frac{\sqrt{10}}{2}+2\approx 3.58113883\text{, }b=-\frac{\sqrt{10}}{2}+2\approx 0.41886117$$

$$a=-\frac{\sqrt{10}}{2}+2\approx 0.41886117\text{, }b=\frac{\sqrt{10}}{2}+2\approx 3.58113883$$

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

Hei whakaoti i ētahi whārite takirua mā te whakakapinga, me whakaoti tētahi whārite i te tuatahi mō tētahi o ngā taurangi. Ka whakakapi i te otinga mō taua taurangi ki tērā o ngā whārite.

$$a+b=4,b^{2}+a^{2}=13$$

Whakaotia te a+b=4 mō a mā te wehe i te a i te taha mauī o te tohu ōrite.

$$a+b=4$$

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

$$a=-b+4$$

Whakakapia te -b+4 mō te a ki tērā atu whārite, b^{2}+a^{2}=13.

$$b^{2}+\left(-b+4\right)^{2}=13$$

Pūrua -b+4.

$$b^{2}+b^{2}-8b+16=13$$

Tāpiri b^{2} ki te b^{2}.

$$2b^{2}-8b+16=13$$

Me tango 13 mai i ngā taha e rua o te whārite.

$$2b^{2}-8b+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\left(-1\right)^{2} mō a, 1\times 4\left(-1\right)\times 2 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\times 3}}{2\times 2}$$

Pūrua 1\times 4\left(-1\right)\times 2.

$$b=\frac{-\left(-8\right)±\sqrt{64-4\times 2\times 3}}{2\times 2}$$

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

$$b=\frac{-\left(-8\right)±\sqrt{64-8\times 3}}{2\times 2}$$

Whakareatia -8 ki te 3.

$$b=\frac{-\left(-8\right)±\sqrt{64-24}}{2\times 2}$$

Tāpiri 64 ki te -24.

$$b=\frac{-\left(-8\right)±\sqrt{40}}{2\times 2}$$

Tuhia te pūtakerua o te 40.

$$b=\frac{-\left(-8\right)±2\sqrt{10}}{2\times 2}$$

Ko te tauaro o 1\times 4\left(-1\right)\times 2 ko 8.

$$b=\frac{8±2\sqrt{10}}{2\times 2}$$

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

$$b=\frac{8±2\sqrt{10}}{4}$$

Nā, me whakaoti te whārite b=\frac{8±2\sqrt{10}}{4} ina he tāpiri te ±. Tāpiri 8 ki te 2\sqrt{10}.

$$b=\frac{2\sqrt{10}+8}{4}$$

Whakawehe 8+2\sqrt{10} ki te 4.

$$b=\frac{\sqrt{10}}{2}+2$$

Nā, me whakaoti te whārite b=\frac{8±2\sqrt{10}}{4} ina he tango te ±. Tango 2\sqrt{10} mai i 8.

$$b=\frac{8-2\sqrt{10}}{4}$$

Whakawehe 8-2\sqrt{10} ki te 4.

$$b=-\frac{\sqrt{10}}{2}+2$$

E rua ngā otinga mō b: 2+\frac{\sqrt{10}}{2} me 2-\frac{\sqrt{10}}{2}. Me whakakapi 2+\frac{\sqrt{10}}{2} mō b ki te whārite a=-b+4 hei kimi i te otinga hāngai mō a e pai ai ki ngā whārite e rua.

$$a=-\left(\frac{\sqrt{10}}{2}+2\right)+4$$

Me whakakapi te 2-\frac{\sqrt{10}}{2} ināianei mō te b ki te whārite a=-b+4 ka whakaoti hei kimi i te otinga hāngai mō a e pai ai ki ngā whārite e rua.

$$a=-\left(-\frac{\sqrt{10}}{2}+2\right)+4$$

Kua oti te pūnaha te whakatau.

$$a=-\left(\frac{\sqrt{10}}{2}+2\right)+4,b=\frac{\sqrt{10}}{2}+2\text{ or }a=-\left(-\frac{\sqrt{10}}{2}+2\right)+4,b=-\frac{\sqrt{10}}{2}+2$$