Whakaoti i te {l}{x^2+y^2=2}{x-y=1}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 2 } \\ { x - y = 1 } \end{array} \right.$$

Whakaoti mō x, y

$$x=\frac{1-\sqrt{3}}{2}\approx -0.366025404\text{, }y=\frac{-\sqrt{3}-1}{2}\approx -1.366025404$$

$$x=\frac{\sqrt{3}+1}{2}\approx 1.366025404\text{, }y=\frac{\sqrt{3}-1}{2}\approx 0.366025404$$

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.

$$x-y=1,y^{2}+x^{2}=2$$

Whakaotia te x-y=1 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x-y=1$$

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

$$x=y+1$$

Whakakapia te y+1 mō te x ki tērā atu whārite, y^{2}+x^{2}=2.

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

Pūrua y+1.

$$y^{2}+y^{2}+2y+1=2$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}+2y+1=2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$2y^{2}+2y-1=0$$

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

$$y=\frac{-2±\sqrt{2^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Pūrua 1\times 1\times 1\times 2.

$$y=\frac{-2±\sqrt{4-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 1+1\times 1^{2}.

$$y=\frac{-2±\sqrt{4-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$y=\frac{-2±\sqrt{4+8}}{2\times 2}$$

Tāpiri 4 ki te 8.

$$y=\frac{-2±\sqrt{12}}{2\times 2}$$

Tuhia te pūtakerua o te 12.

$$y=\frac{-2±2\sqrt{3}}{2\times 2}$$

Whakareatia 2 ki te 1+1\times 1^{2}.

$$y=\frac{-2±2\sqrt{3}}{4}$$

Nā, me whakaoti te whārite y=\frac{-2±2\sqrt{3}}{4} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{3}.

$$y=\frac{2\sqrt{3}-2}{4}$$

Whakawehe -2+2\sqrt{3} ki te 4.

$$y=\frac{\sqrt{3}-1}{2}$$

Nā, me whakaoti te whārite y=\frac{-2±2\sqrt{3}}{4} ina he tango te ±. Tango 2\sqrt{3} mai i -2.

$$y=\frac{-2\sqrt{3}-2}{4}$$

Whakawehe -2-2\sqrt{3} ki te 4.

$$y=\frac{-\sqrt{3}-1}{2}$$

E rua ngā otinga mō y: \frac{-1+\sqrt{3}}{2} me \frac{-1-\sqrt{3}}{2}. Me whakakapi \frac{-1+\sqrt{3}}{2} mō y ki te whārite x=y+1 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=\frac{\sqrt{3}-1}{2}+1$$

Me whakakapi te \frac{-1-\sqrt{3}}{2} ināianei mō te y ki te whārite x=y+1 ka whakaoti hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=\frac{-\sqrt{3}-1}{2}+1$$

Kua oti te pūnaha te whakatau.

$$x=\frac{\sqrt{3}-1}{2}+1,y=\frac{\sqrt{3}-1}{2}\text{ or }x=\frac{-\sqrt{3}-1}{2}+1,y=\frac{-\sqrt{3}-1}{2}$$