Whakaoti i te 99^2+x^2=125^2

$${ 99 }^{ 2 } + { x }^{ 2 } = { 125 }^{ 2 }$$

Whakaoti mō x

$$x=8\sqrt{91}\approx 76.315136113$$

$$x=-8\sqrt{91}\approx -76.315136113$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 99 mā te pū o 2, kia riro ko 9801.

$$9801+x^{2}=125^{2}$$

Tātaihia te 125 mā te pū o 2, kia riro ko 15625.

$$9801+x^{2}=15625$$

Tangohia te 9801 mai i ngā taha e rua.

$$x^{2}=15625-9801$$

Tangohia te 9801 i te 15625, ka 5824.

$$x^{2}=5824$$

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

$$x=8\sqrt{91} x=-8\sqrt{91}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 99 mā te pū o 2, kia riro ko 9801.

$$9801+x^{2}=125^{2}$$

Tātaihia te 125 mā te pū o 2, kia riro ko 15625.

$$9801+x^{2}=15625$$

Tangohia te 15625 mai i ngā taha e rua.

$$9801+x^{2}-15625=0$$

Tangohia te 15625 i te 9801, ka -5824.

$$-5824+x^{2}=0$$

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.

$$x^{2}-5824=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -5824 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5824\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-5824\right)}}{2}$$

Whakareatia -4 ki te -5824.

$$x=\frac{0±\sqrt{23296}}{2}$$

Tuhia te pūtakerua o te 23296.

$$x=\frac{0±16\sqrt{91}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{91}}{2} ina he tāpiri te ±.

$$x=8\sqrt{91}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{91}}{2} ina he tango te ±.

$$x=-8\sqrt{91}$$

Kua oti te whārite te whakatau.

$$x=8\sqrt{91} x=-8\sqrt{91}$$