Whakaoti i te sqrt{2x-3}=6^2x*sqrt{4}

$$\sqrt { 2 x - 3 } = 6 ^ { 2 } x \cdot \sqrt { 4 }$$

Whakaoti mō x (complex solution)

$$x=\frac{1+\sqrt{15551}i}{5184}\approx 0.000192901+0.024055488i$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x-3}\right)^{2}=\left(6^{2}x\sqrt{4}\right)^{2}$$

Tātaihia te \sqrt{2x-3} mā te pū o 2, kia riro ko 2x-3.

$$2x-3=\left(6^{2}x\sqrt{4}\right)^{2}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$2x-3=\left(36x\sqrt{4}\right)^{2}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$2x-3=\left(36x\times 2\right)^{2}$$

Whakareatia te 36 ki te 2, ka 72.

$$2x-3=\left(72x\right)^{2}$$

Whakarohaina te \left(72x\right)^{2}.

$$2x-3=72^{2}x^{2}$$

Tātaihia te 72 mā te pū o 2, kia riro ko 5184.

$$2x-3=5184x^{2}$$

Tangohia te 5184x^{2} mai i ngā taha e rua.

$$2x-3-5184x^{2}=0$$

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.

$$-5184x^{2}+2x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5184 mō a, 2 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-5184\right)\left(-3\right)}}{2\left(-5184\right)}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-5184\right)\left(-3\right)}}{2\left(-5184\right)}$$

Whakareatia -4 ki te -5184.

$$x=\frac{-2±\sqrt{4+20736\left(-3\right)}}{2\left(-5184\right)}$$

Whakareatia 20736 ki te -3.

$$x=\frac{-2±\sqrt{4-62208}}{2\left(-5184\right)}$$

Tāpiri 4 ki te -62208.

$$x=\frac{-2±\sqrt{-62204}}{2\left(-5184\right)}$$

Tuhia te pūtakerua o te -62204.

$$x=\frac{-2±2\sqrt{15551}i}{2\left(-5184\right)}$$

Whakareatia 2 ki te -5184.

$$x=\frac{-2±2\sqrt{15551}i}{-10368}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{15551}i}{-10368} ina he tāpiri te ±. Tāpiri -2 ki te 2i\sqrt{15551}.

$$x=\frac{-2+2\sqrt{15551}i}{-10368}$$

Whakawehe -2+2i\sqrt{15551} ki te -10368.

$$x=\frac{-\sqrt{15551}i+1}{5184}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{15551}i}{-10368} ina he tango te ±. Tango 2i\sqrt{15551} mai i -2.

$$x=\frac{-2\sqrt{15551}i-2}{-10368}$$

Whakawehe -2-2i\sqrt{15551} ki te -10368.

$$x=\frac{1+\sqrt{15551}i}{5184}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{15551}i+1}{5184} x=\frac{1+\sqrt{15551}i}{5184}$$

Whakakapia te \frac{-\sqrt{15551}i+1}{5184} mō te x i te whārite \sqrt{2x-3}=6^{2}x\sqrt{4}.

$$\sqrt{2\times \frac{-\sqrt{15551}i+1}{5184}-3}=6^{2}\times \frac{-\sqrt{15551}i+1}{5184}\sqrt{4}$$

Whakarūnātia. Ko te uara x=\frac{-\sqrt{15551}i+1}{5184} kāore e ngata ana ki te whārite.

$$-\left(\frac{1}{72}-\frac{1}{72}i\times 15551^{\frac{1}{2}}\right)=-\frac{1}{72}i\times 15551^{\frac{1}{2}}+\frac{1}{72}$$

Whakakapia te \frac{1+\sqrt{15551}i}{5184} mō te x i te whārite \sqrt{2x-3}=6^{2}x\sqrt{4}.

$$\sqrt{2\times \frac{1+\sqrt{15551}i}{5184}-3}=6^{2}\times \frac{1+\sqrt{15551}i}{5184}\sqrt{4}$$

Whakarūnātia. Ko te uara x=\frac{1+\sqrt{15551}i}{5184} kua ngata te whārite.

$$\frac{1}{72}+\frac{1}{72}i\times 15551^{\frac{1}{2}}=\frac{1}{72}+\frac{1}{72}i\times 15551^{\frac{1}{2}}$$

Ko te whārite \sqrt{2x-3}=36\sqrt{4}x he rongoā ahurei.

$$x=\frac{1+\sqrt{15551}i}{5184}$$