Whakaoti i te 25^2/75^2+x^2/45=1

$$\frac{ { 25 }^{ 2 } }{ { 75 }^{ 2 } } + \frac{ { x }^{ 2 } }{ 45 } =1$$

Whakaoti mō x

$$x=2\sqrt{10}\approx 6.32455532$$

$$x=-2\sqrt{10}\approx -6.32455532$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 45.

$$\frac{1}{125}\times 25^{2}+x^{2}=45$$

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$\frac{1}{125}\times 625+x^{2}=45$$

Whakareatia te \frac{1}{125} ki te 625, ka 5.

$$5+x^{2}=45$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}=45-5$$

Tangohia te 5 i te 45, ka 40.

$$x^{2}=40$$

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

$$x=2\sqrt{10} x=-2\sqrt{10}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 45.

$$\frac{1}{125}\times 25^{2}+x^{2}=45$$

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$\frac{1}{125}\times 625+x^{2}=45$$

Whakareatia te \frac{1}{125} ki te 625, ka 5.

$$5+x^{2}=45$$

Tangohia te 45 mai i ngā taha e rua.

$$5+x^{2}-45=0$$

Tangohia te 45 i te 5, ka -40.

$$-40+x^{2}=0$$

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.

$$x^{2}-40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-40\right)}}{2}$$

Whakareatia -4 ki te -40.

$$x=\frac{0±\sqrt{160}}{2}$$

Tuhia te pūtakerua o te 160.

$$x=\frac{0±4\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{2} ina he tāpiri te ±.

$$x=2\sqrt{10}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{2} ina he tango te ±.

$$x=-2\sqrt{10}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{10} x=-2\sqrt{10}$$