Whakaoti i te a^2/36+frac{{left(sqrt{155+3}right)}^2}{9}=1

$$\frac{ { a }^{ 2 } }{ 36 } + \frac{ { \left( \sqrt{ 155+3 } \right) }^{ 2 } }{ 9 } = 1$$

Whakaoti mō a

$$a=-2\sqrt{149}i\approx -0-24.413111231i$$

$$a=2\sqrt{149}i\approx 24.413111231i$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 36,9.

$$a^{2}+4\left(\sqrt{155+3}\right)^{2}=36$$

Tāpirihia te 155 ki te 3, ka 158.

$$a^{2}+4\left(\sqrt{158}\right)^{2}=36$$

Ko te pūrua o \sqrt{158} ko 158.

$$a^{2}+4\times 158=36$$

Whakareatia te 4 ki te 158, ka 632.

$$a^{2}+632=36$$

Tangohia te 632 mai i ngā taha e rua.

$$a^{2}=36-632$$

Tangohia te 632 i te 36, ka -596.

$$a^{2}=-596$$

Kua oti te whārite te whakatau.

$$a=2\sqrt{149}i a=-2\sqrt{149}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 36,9.

$$a^{2}+4\left(\sqrt{155+3}\right)^{2}=36$$

Tāpirihia te 155 ki te 3, ka 158.

$$a^{2}+4\left(\sqrt{158}\right)^{2}=36$$

Ko te pūrua o \sqrt{158} ko 158.

$$a^{2}+4\times 158=36$$

Whakareatia te 4 ki te 158, ka 632.

$$a^{2}+632=36$$

Tangohia te 36 mai i ngā taha e rua.

$$a^{2}+632-36=0$$

Tangohia te 36 i te 632, ka 596.

$$a^{2}+596=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 596 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 596}}{2}$$

Pūrua 0.

$$a=\frac{0±\sqrt{-4\times 596}}{2}$$

Whakareatia -4 ki te 596.

$$a=\frac{0±\sqrt{-2384}}{2}$$

Tuhia te pūtakerua o te -2384.

$$a=\frac{0±4\sqrt{149}i}{2}$$

Nā, me whakaoti te whārite a=\frac{0±4\sqrt{149}i}{2} ina he tāpiri te ±.

$$a=2\sqrt{149}i$$

Nā, me whakaoti te whārite a=\frac{0±4\sqrt{149}i}{2} ina he tango te ±.

$$a=-2\sqrt{149}i$$

Kua oti te whārite te whakatau.

$$a=2\sqrt{149}i a=-2\sqrt{149}i$$