Whakaoti i te 5/w^2-32=6/w^2+56

$$\frac { 5 } { w ^ { 2 } } - 32 = \frac { 6 } { w ^ { 2 } } + 56$$

Whakaoti mō w

$$w=-\frac{\sqrt{22}i}{44}\approx -0-0.106600358i$$

$$w=\frac{\sqrt{22}i}{44}\approx 0.106600358i$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe w ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te w^{2}.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Tangohia te w^{2}\times 56 mai i ngā taha e rua.

$$5+w^{2}\left(-32\right)-w^{2}\times 56=6$$

Pahekotia te w^{2}\left(-32\right) me -w^{2}\times 56, ka -88w^{2}.

$$5-88w^{2}=6$$

Tangohia te 5 mai i ngā taha e rua.

$$-88w^{2}=6-5$$

Tangohia te 5 i te 6, ka 1.

$$-88w^{2}=1$$

Whakawehea ngā taha e rua ki te -88.

$$w^{2}=-\frac{1}{88}$$

Kua oti te whārite te whakatau.

$$w=\frac{\sqrt{22}i}{44} w=-\frac{\sqrt{22}i}{44}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe w ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te w^{2}.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Tangohia te 6 mai i ngā taha e rua.

$$5+w^{2}\left(-32\right)-6=w^{2}\times 56$$

Tangohia te 6 i te 5, ka -1.

$$-1+w^{2}\left(-32\right)=w^{2}\times 56$$

Tangohia te w^{2}\times 56 mai i ngā taha e rua.

$$-1+w^{2}\left(-32\right)-w^{2}\times 56=0$$

Pahekotia te w^{2}\left(-32\right) me -w^{2}\times 56, ka -88w^{2}.

$$-1-88w^{2}=0$$

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.

$$-88w^{2}-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -88 mō a, 0 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

Pūrua 0.

$$w=\frac{0±\sqrt{-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

Whakareatia -4 ki te -88.

$$w=\frac{0±\sqrt{352\left(-1\right)}}{2\left(-88\right)}$$

Whakareatia 352 ki te -1.

$$w=\frac{0±\sqrt{-352}}{2\left(-88\right)}$$

Tuhia te pūtakerua o te -352.

$$w=\frac{0±4\sqrt{22}i}{2\left(-88\right)}$$

Whakareatia 2 ki te -88.

$$w=\frac{0±4\sqrt{22}i}{-176}$$

Nā, me whakaoti te whārite w=\frac{0±4\sqrt{22}i}{-176} ina he tāpiri te ±.

$$w=-\frac{\sqrt{22}i}{44}$$

Nā, me whakaoti te whārite w=\frac{0±4\sqrt{22}i}{-176} ina he tango te ±.

$$w=\frac{\sqrt{22}i}{44}$$

Kua oti te whārite te whakatau.

$$w=-\frac{\sqrt{22}i}{44} w=\frac{\sqrt{22}i}{44}$$