Whakaoti i te 7^2+x^2=11^2

$${ 7 }^{ 2 } + { x }^{ 2 } = { 11 }^{ 2 }$$

Whakaoti mō x

$$x=6\sqrt{2}\approx 8.485281374$$

$$x=-6\sqrt{2}\approx -8.485281374$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49+x^{2}=11^{2}$$

Tātaihia te 11 mā te pū o 2, kia riro ko 121.

$$49+x^{2}=121$$

Tangohia te 49 mai i ngā taha e rua.

$$x^{2}=121-49$$

Tangohia te 49 i te 121, ka 72.

$$x^{2}=72$$

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

$$x=6\sqrt{2} x=-6\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49+x^{2}=11^{2}$$

Tātaihia te 11 mā te pū o 2, kia riro ko 121.

$$49+x^{2}=121$$

Tangohia te 121 mai i ngā taha e rua.

$$49+x^{2}-121=0$$

Tangohia te 121 i te 49, ka -72.

$$-72+x^{2}=0$$

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.

$$x^{2}-72=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -72 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-72\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-72\right)}}{2}$$

Whakareatia -4 ki te -72.

$$x=\frac{0±\sqrt{288}}{2}$$

Tuhia te pūtakerua o te 288.

$$x=\frac{0±12\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{2} ina he tāpiri te ±.

$$x=6\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{2} ina he tango te ±.

$$x=-6\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=6\sqrt{2} x=-6\sqrt{2}$$