Whakaoti i te 105r^230=7065

$$105 r ^ { 2 } 30 = 7065$$

Whakaoti mō r

$$r = \frac{\sqrt{10990}}{70} \approx 1.497617155$$

$$r = -\frac{\sqrt{10990}}{70} \approx -1.497617155$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 105 ki te 30, ka 3150.

$$3150r^{2}=7065$$

Whakawehea ngā taha e rua ki te 3150.

$$r^{2}=\frac{7065}{3150}$$

Whakahekea te hautanga \frac{7065}{3150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 45.

$$r^{2}=\frac{157}{70}$$

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

$$r=\frac{\sqrt{10990}}{70} r=-\frac{\sqrt{10990}}{70}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 105 ki te 30, ka 3150.

$$3150r^{2}=7065$$

Tangohia te 7065 mai i ngā taha e rua.

$$3150r^{2}-7065=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3150 mō a, 0 mō b, me -7065 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 3150\left(-7065\right)}}{2\times 3150}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\times 3150\left(-7065\right)}}{2\times 3150}$$

Whakareatia -4 ki te 3150.

$$r=\frac{0±\sqrt{-12600\left(-7065\right)}}{2\times 3150}$$

Whakareatia -12600 ki te -7065.

$$r=\frac{0±\sqrt{89019000}}{2\times 3150}$$

Tuhia te pūtakerua o te 89019000.

$$r=\frac{0±90\sqrt{10990}}{2\times 3150}$$

Whakareatia 2 ki te 3150.

$$r=\frac{0±90\sqrt{10990}}{6300}$$

Nā, me whakaoti te whārite r=\frac{0±90\sqrt{10990}}{6300} ina he tāpiri te ±.

$$r=\frac{\sqrt{10990}}{70}$$

Nā, me whakaoti te whārite r=\frac{0±90\sqrt{10990}}{6300} ina he tango te ±.

$$r=-\frac{\sqrt{10990}}{70}$$

Kua oti te whārite te whakatau.

$$r=\frac{\sqrt{10990}}{70} r=-\frac{\sqrt{10990}}{70}$$