Whakaoti i te sqrt{4n+3}=n

$$\sqrt{ 4n+3 } = n$$

Whakaoti mō n

$$n=\sqrt{7}+2\approx 4.645751311$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{4n+3} mā te pū o 2, kia riro ko 4n+3.

$$4n+3=n^{2}$$

Tangohia te n^{2} mai i ngā taha e rua.

$$4n+3-n^{2}=0$$

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.

$$-n^{2}+4n+3=0$$

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

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

Pūrua 4.

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

Whakareatia -4 ki te -1.

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

Whakareatia 4 ki te 3.

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

Tāpiri 16 ki te 12.

$$n=\frac{-4±\sqrt{28}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 28.

$$n=\frac{-4±2\sqrt{7}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$n=\frac{-4±2\sqrt{7}}{-2}$$

Nā, me whakaoti te whārite n=\frac{-4±2\sqrt{7}}{-2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{7}.

$$n=\frac{2\sqrt{7}-4}{-2}$$

Whakawehe -4+2\sqrt{7} ki te -2.

$$n=2-\sqrt{7}$$

Nā, me whakaoti te whārite n=\frac{-4±2\sqrt{7}}{-2} ina he tango te ±. Tango 2\sqrt{7} mai i -4.

$$n=\frac{-2\sqrt{7}-4}{-2}$$

Whakawehe -4-2\sqrt{7} ki te -2.

$$n=\sqrt{7}+2$$

Kua oti te whārite te whakatau.

$$n=2-\sqrt{7} n=\sqrt{7}+2$$

Whakakapia te 2-\sqrt{7} mō te n i te whārite \sqrt{4n+3}=n.

$$\sqrt{4\left(2-\sqrt{7}\right)+3}=2-\sqrt{7}$$

Whakarūnātia. Ko te uara n=2-\sqrt{7} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$7^{\frac{1}{2}}-2=2-7^{\frac{1}{2}}$$

Whakakapia te \sqrt{7}+2 mō te n i te whārite \sqrt{4n+3}=n.

$$\sqrt{4\left(\sqrt{7}+2\right)+3}=\sqrt{7}+2$$

Whakarūnātia. Ko te uara n=\sqrt{7}+2 kua ngata te whārite.

$$2+7^{\frac{1}{2}}=2+7^{\frac{1}{2}}$$

Ko te whārite \sqrt{4n+3}=n he rongoā ahurei.

$$n=\sqrt{7}+2$$