Whakaoti i te lambda^2-4999001lambda/100000+0000225=0

$$\lambda ^ { 2 } - \frac { 4999001 \lambda } { 100000 } + 0000225 = 0$$

Whakaoti mō λ

$$\lambda =\frac{4999001}{100000}=49.99001$$

$$\lambda =0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia ngā taha e rua o te whārite ki te 100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Whakareatia te 0 ki te 225, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$100000\lambda ^{2}-4999001\lambda =0$$

Tauwehea te \lambda .

$$\lambda \left(100000\lambda -4999001\right)=0$$

Hei kimi otinga whārite, me whakaoti te \lambda =0 me te 100000\lambda -4999001=0.

$$\lambda =0 \lambda =\frac{4999001}{100000}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Whakareatia te 0 ki te 225, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$100000\lambda ^{2}-4999001\lambda =0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100000 mō a, -4999001 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\lambda =\frac{-\left(-4999001\right)±\sqrt{\left(-4999001\right)^{2}}}{2\times 100000}$$

Tuhia te pūtakerua o te \left(-4999001\right)^{2}.

$$\lambda =\frac{-\left(-4999001\right)±4999001}{2\times 100000}$$

Ko te tauaro o -4999001 ko 4999001.

$$\lambda =\frac{4999001±4999001}{2\times 100000}$$

Whakareatia 2 ki te 100000.

$$\lambda =\frac{4999001±4999001}{200000}$$

Nā, me whakaoti te whārite \lambda =\frac{4999001±4999001}{200000} ina he tāpiri te ±. Tāpiri 4999001 ki te 4999001.

$$\lambda =\frac{9998002}{200000}$$

Whakahekea te hautanga \frac{9998002}{200000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\lambda =\frac{4999001}{100000}$$

Nā, me whakaoti te whārite \lambda =\frac{4999001±4999001}{200000} ina he tango te ±. Tango 4999001 mai i 4999001.

$$\lambda =\frac{0}{200000}$$

Whakawehe 0 ki te 200000.

$$\lambda =0$$

Kua oti te whārite te whakatau.

$$\lambda =\frac{4999001}{100000} \lambda =0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Whakareatia te 0 ki te 0, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Whakareatia te 0 ki te 225, ka 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$100000\lambda ^{2}-4999001\lambda =0$$

Whakawehea ngā taha e rua ki te 100000.

$$\frac{100000\lambda ^{2}-4999001\lambda }{100000}=\frac{0}{100000}$$

Mā te whakawehe ki te 100000 ka wetekia te whakareanga ki te 100000.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =\frac{0}{100000}$$

Whakawehe 0 ki te 100000.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =0$$

Whakawehea te -\frac{4999001}{100000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{4999001}{200000}. Nā, tāpiria te pūrua o te -\frac{4999001}{200000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\left(-\frac{4999001}{200000}\right)^{2}=\left(-\frac{4999001}{200000}\right)^{2}$$

Pūruatia -\frac{4999001}{200000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000}=\frac{24990010998001}{40000000000}$$

Tauwehea \lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000}. 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}.

$$\left(\lambda -\frac{4999001}{200000}\right)^{2}=\frac{24990010998001}{40000000000}$$

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

$$\sqrt{\left(\lambda -\frac{4999001}{200000}\right)^{2}}=\sqrt{\frac{24990010998001}{40000000000}}$$

Whakarūnātia.

$$\lambda -\frac{4999001}{200000}=\frac{4999001}{200000} \lambda -\frac{4999001}{200000}=-\frac{4999001}{200000}$$

Me tāpiri \frac{4999001}{200000} ki ngā taha e rua o te whārite.

$$\lambda =\frac{4999001}{100000} \lambda =0$$