Whakaoti i te 9.9^2+x^2=12.5^2

$${ 9.9 }^{ 2 } + { x }^{ 2 } = { 12.5 }^{ 2 }$$

Whakaoti mō x

$$x = \frac{4 \sqrt{91}}{5} \approx 7.631513611$$

$$x = -\frac{4 \sqrt{91}}{5} \approx -7.631513611$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 9.9 mā te pū o 2, kia riro ko 98.01.

$$98.01+x^{2}=12.5^{2}$$

Tātaihia te 12.5 mā te pū o 2, kia riro ko 156.25.

$$98.01+x^{2}=156.25$$

Tangohia te 98.01 mai i ngā taha e rua.

$$x^{2}=156.25-98.01$$

Tangohia te 98.01 i te 156.25, ka 58.24.

$$x^{2}=58.24$$

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

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 9.9 mā te pū o 2, kia riro ko 98.01.

$$98.01+x^{2}=12.5^{2}$$

Tātaihia te 12.5 mā te pū o 2, kia riro ko 156.25.

$$98.01+x^{2}=156.25$$

Tangohia te 156.25 mai i ngā taha e rua.

$$98.01+x^{2}-156.25=0$$

Tangohia te 156.25 i te 98.01, ka -58.24.

$$-58.24+x^{2}=0$$

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.

$$x^{2}-58.24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -58.24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-58.24\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-58.24\right)}}{2}$$

Whakareatia -4 ki te -58.24.

$$x=\frac{0±\sqrt{232.96}}{2}$$

Tuhia te pūtakerua o te 232.96.

$$x=\frac{0±\frac{8\sqrt{91}}{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8\sqrt{91}}{5}}{2} ina he tāpiri te ±.

$$x=\frac{4\sqrt{91}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8\sqrt{91}}{5}}{2} ina he tango te ±.

$$x=-\frac{4\sqrt{91}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$