Whakaoti i te (x)=sqrt{4x-20}

$$( x ) = \sqrt { 4 x - 20 }$$

Whakaoti mō x (complex solution)

$$x=2-4i$$

$$x=2+4i$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$x^{2}=\left(\sqrt{4x-20}\right)^{2}$$

Tātaihia te \sqrt{4x-20} mā te pū o 2, kia riro ko 4x-20.

$$x^{2}=4x-20$$

Tangohia te 4x mai i ngā taha e rua.

$$x^{2}-4x=-20$$

Me tāpiri te 20 ki ngā taha e rua.

$$x^{2}-4x+20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me 20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 20}}{2}$$

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 20}}{2}$$

Whakareatia -4 ki te 20.

$$x=\frac{-\left(-4\right)±\sqrt{16-80}}{2}$$

Tāpiri 16 ki te -80.

$$x=\frac{-\left(-4\right)±\sqrt{-64}}{2}$$

Tuhia te pūtakerua o te -64.

$$x=\frac{-\left(-4\right)±8i}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±8i}{2}$$

Nā, me whakaoti te whārite x=\frac{4±8i}{2} ina he tāpiri te ±. Tāpiri 4 ki te 8i.

$$x=\frac{4+8i}{2}$$

Whakawehe 4+8i ki te 2.

$$x=2+4i$$

Nā, me whakaoti te whārite x=\frac{4±8i}{2} ina he tango te ±. Tango 8i mai i 4.

$$x=\frac{4-8i}{2}$$

Whakawehe 4-8i ki te 2.

$$x=2-4i$$

Kua oti te whārite te whakatau.

$$x=2+4i x=2-4i$$

Whakakapia te 2+4i mō te x i te whārite x=\sqrt{4x-20}.

$$2+4i=\sqrt{4\left(2+4i\right)-20}$$

Whakarūnātia. Ko te uara x=2+4i kua ngata te whārite.

$$2+4i=2+4i$$

Whakakapia te 2-4i mō te x i te whārite x=\sqrt{4x-20}.

$$2-4i=\sqrt{4\left(2-4i\right)-20}$$

Whakarūnātia. Ko te uara x=2-4i kua ngata te whārite.

$$2-4i=2-4i$$

Rārangihia ngā rongoā katoa o x=\sqrt{4x-20}.

$$x=2+4i x=2-4i$$