Whakaoti i te x^2=18^2-100/9

$${ x }^{ 2 } = { 18 }^{ 2 } - \frac{ 100 }{ 9 }$$

Whakaoti mō x

$$x = \frac{16 \sqrt{11}}{3} \approx 17.688665549$$

$$x = -\frac{16 \sqrt{11}}{3} \approx -17.688665549$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 18 mā te pū o 2, kia riro ko 324.

$$x^{2}=324-\frac{100}{9}$$

Tangohia te \frac{100}{9} i te 324, ka \frac{2816}{9}.

$$x^{2}=\frac{2816}{9}$$

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

$$x=\frac{16\sqrt{11}}{3} x=-\frac{16\sqrt{11}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 18 mā te pū o 2, kia riro ko 324.

$$x^{2}=324-\frac{100}{9}$$

Tangohia te \frac{100}{9} i te 324, ka \frac{2816}{9}.

$$x^{2}=\frac{2816}{9}$$

Tangohia te \frac{2816}{9} mai i ngā taha e rua.

$$x^{2}-\frac{2816}{9}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{2816}{9} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2816}{9}\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2816}{9}\right)}}{2}$$

Whakareatia -4 ki te -\frac{2816}{9}.

$$x=\frac{0±\sqrt{\frac{11264}{9}}}{2}$$

Tuhia te pūtakerua o te \frac{11264}{9}.

$$x=\frac{0±\frac{32\sqrt{11}}{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{32\sqrt{11}}{3}}{2} ina he tāpiri te ±.

$$x=\frac{16\sqrt{11}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{32\sqrt{11}}{3}}{2} ina he tango te ±.

$$x=-\frac{16\sqrt{11}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{16\sqrt{11}}{3} x=-\frac{16\sqrt{11}}{3}$$