Whakaoti i te 2(r^2+3)=108

$$2 ( r ^ { 2 } + 3 ) = 108$$

Whakaoti mō r

$$r=\sqrt{51}\approx 7.141428429$$

$$r=-\sqrt{51}\approx -7.141428429$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 2.

$$r^{2}+3=\frac{108}{2}$$

Whakawehea te 108 ki te 2, kia riro ko 54.

$$r^{2}+3=54$$

Tangohia te 3 mai i ngā taha e rua.

$$r^{2}=54-3$$

Tangohia te 3 i te 54, ka 51.

$$r^{2}=51$$

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

$$r=\sqrt{51} r=-\sqrt{51}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 2.

$$r^{2}+3=\frac{108}{2}$$

Whakawehea te 108 ki te 2, kia riro ko 54.

$$r^{2}+3=54$$

Tangohia te 54 mai i ngā taha e rua.

$$r^{2}+3-54=0$$

Tangohia te 54 i te 3, ka -51.

$$r^{2}-51=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -51 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-51\right)}}{2}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\left(-51\right)}}{2}$$

Whakareatia -4 ki te -51.

$$r=\frac{0±\sqrt{204}}{2}$$

Tuhia te pūtakerua o te 204.

$$r=\frac{0±2\sqrt{51}}{2}$$

Nā, me whakaoti te whārite r=\frac{0±2\sqrt{51}}{2} ina he tāpiri te ±.

$$r=\sqrt{51}$$

Nā, me whakaoti te whārite r=\frac{0±2\sqrt{51}}{2} ina he tango te ±.

$$r=-\sqrt{51}$$

Kua oti te whārite te whakatau.

$$r=\sqrt{51} r=-\sqrt{51}$$