Whakaoti i te 3+12=1/2*98r^2

$$3 + 12 = \frac { 1 } { 2 } \times 98 r ^ { 2 }$$

Whakaoti mō r

$$r=\frac{\sqrt{15}}{7}\approx 0.553283335$$

$$r=-\frac{\sqrt{15}}{7}\approx -0.553283335$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te 3 ki te 12, ka 15.

$$15=\frac{1}{2}\times 98r^{2}$$

Whakareatia te \frac{1}{2} ki te 98, ka 49.

$$15=49r^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49r^{2}=15$$

Whakawehea ngā taha e rua ki te 49.

$$r^{2}=\frac{15}{49}$$

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

$$r=\frac{\sqrt{15}}{7} r=-\frac{\sqrt{15}}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 3 ki te 12, ka 15.

$$15=\frac{1}{2}\times 98r^{2}$$

Whakareatia te \frac{1}{2} ki te 98, ka 49.

$$15=49r^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49r^{2}=15$$

Tangohia te 15 mai i ngā taha e rua.

$$49r^{2}-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 49 mō a, 0 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 49\left(-15\right)}}{2\times 49}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\times 49\left(-15\right)}}{2\times 49}$$

Whakareatia -4 ki te 49.

$$r=\frac{0±\sqrt{-196\left(-15\right)}}{2\times 49}$$

Whakareatia -196 ki te -15.

$$r=\frac{0±\sqrt{2940}}{2\times 49}$$

Tuhia te pūtakerua o te 2940.

$$r=\frac{0±14\sqrt{15}}{2\times 49}$$

Whakareatia 2 ki te 49.

$$r=\frac{0±14\sqrt{15}}{98}$$

Nā, me whakaoti te whārite r=\frac{0±14\sqrt{15}}{98} ina he tāpiri te ±.

$$r=\frac{\sqrt{15}}{7}$$

Nā, me whakaoti te whārite r=\frac{0±14\sqrt{15}}{98} ina he tango te ±.

$$r=-\frac{\sqrt{15}}{7}$$

Kua oti te whārite te whakatau.

$$r=\frac{\sqrt{15}}{7} r=-\frac{\sqrt{15}}{7}$$