Whakaoti i te 68x^2=120-33sqrt{15}

$$68 { x }^{ 2 } =120-33 \sqrt{ 15 }$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}\approx -0-0.338865981i$$

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34}\approx 0.338865981i$$

Ngā Upane mā te Kimi Pūtakerua

Mā te whakawehe ki te 68 ka wetekia te whakareanga ki te 68.

$$x^{2}=\frac{120-33\sqrt{15}}{68}$$

Whakawehe 120-33\sqrt{15} ki te 68.

$$x^{2}=-\frac{33\sqrt{15}}{68}+\frac{30}{17}$$

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

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34} x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 120 mai i ngā taha e rua.

$$68x^{2}-120=-33\sqrt{15}$$

Me tāpiri te 33\sqrt{15} ki ngā taha e rua.

$$68x^{2}-120+33\sqrt{15}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$68x^{2}+33\sqrt{15}-120=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 68 mō a, 0 mō b, me -120+33\sqrt{15} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 68\left(33\sqrt{15}-120\right)}}{2\times 68}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 68\left(33\sqrt{15}-120\right)}}{2\times 68}$$

Whakareatia -4 ki te 68.

$$x=\frac{0±\sqrt{-272\left(33\sqrt{15}-120\right)}}{2\times 68}$$

Whakareatia -272 ki te -120+33\sqrt{15}.

$$x=\frac{0±\sqrt{32640-8976\sqrt{15}}}{2\times 68}$$

Tuhia te pūtakerua o te 32640-8976\sqrt{15}.

$$x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{2\times 68}$$

Whakareatia 2 ki te 68.

$$x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136}$$

Nā, me whakaoti te whārite x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136} ina he tāpiri te ±.

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

Nā, me whakaoti te whārite x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136} ina he tango te ±.

$$x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

Kua oti te whārite te whakatau.

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34} x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$