Whakaoti i te 4a-a^2=3sqrt{3}

$$4 a - a ^ { 2 } = 3 \sqrt { 3 }$$

Whakaoti mō a

$$a=-i\sqrt{3\sqrt{3}-4}+2\approx 2-1.093687534i$$

$$a=2+i\sqrt{3\sqrt{3}-4}\approx 2+1.093687534i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-a^{2}+4a=3\sqrt{3}$$

Me tango 3\sqrt{3} mai i ngā taha e rua o te whārite.

$$-a^{2}+4a-3\sqrt{3}=3\sqrt{3}-3\sqrt{3}$$

Mā te tango i te 3\sqrt{3} i a ia ake anō ka toe ko te 0.

$$-a^{2}+4a-3\sqrt{3}=0$$

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

$$a=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-3\sqrt{3}\right)}}{2\left(-1\right)}$$

Pūrua 4.

$$a=\frac{-4±\sqrt{16-4\left(-1\right)\left(-3\sqrt{3}\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-4±\sqrt{16+4\left(-3\sqrt{3}\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -3\sqrt{3}.

$$a=\frac{-4±\sqrt{16-12\sqrt{3}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 16-12\sqrt{3}.

$$a=\frac{-4±2i\sqrt{-\left(4-3\sqrt{3}\right)}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{-4±2i\sqrt{-\left(4-3\sqrt{3}\right)}}{-2}$$

Nā, me whakaoti te whārite a=\frac{-4±2i\sqrt{-\left(4-3\sqrt{3}\right)}}{-2} ina he tāpiri te ±. Tāpiri -4 ki te 2i\sqrt{-\left(4-3\sqrt{3}\right)}.

$$a=\frac{-4+2i\sqrt{3\sqrt{3}-4}}{-2}$$

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

$$a=-i\sqrt{3\sqrt{3}-4}+2$$

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

$$a=\frac{-2i\sqrt{3\sqrt{3}-4}-4}{-2}$$

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

$$a=2+i\sqrt{3\sqrt{3}-4}$$

Kua oti te whārite te whakatau.

$$a=-i\sqrt{3\sqrt{3}-4}+2 a=2+i\sqrt{3\sqrt{3}-4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-a^{2}+4a=3\sqrt{3}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-a^{2}+4a}{-1}=\frac{3\sqrt{3}}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$a^{2}+\frac{4}{-1}a=\frac{3\sqrt{3}}{-1}$$

Whakawehe 4 ki te -1.

$$a^{2}-4a=\frac{3\sqrt{3}}{-1}$$

Whakawehe 3\sqrt{3} ki te -1.

$$a^{2}-4a=-3\sqrt{3}$$

Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūrua -2.

$$a^{2}-4a+4=-3\sqrt{3}+4$$

Tāpiri -3\sqrt{3} ki te 4.

$$a^{2}-4a+4=4-3\sqrt{3}$$

Tauwehea a^{2}-4a+4. 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}.

$$\left(a-2\right)^{2}=4-3\sqrt{3}$$

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

$$\sqrt{\left(a-2\right)^{2}}=\sqrt{4-3\sqrt{3}}$$

Whakarūnātia.

$$a-2=i\sqrt{-\left(4-3\sqrt{3}\right)} a-2=-i\sqrt{3\sqrt{3}-4}$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$a=2+i\sqrt{3\sqrt{3}-4} a=-i\sqrt{3\sqrt{3}-4}+2$$