Whakaoti i te 100^2+100+8=3p^2-190+11

$$100 ^ { 2 } + 100 + 8 = 3 p ^ { 2 } - 190 + 11$$

Whakaoti mō p

$$p=3\sqrt{381}\approx 58.557663888$$

$$p=-3\sqrt{381}\approx -58.557663888$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$10000+100+8=3p^{2}-190+11$$

Tāpirihia te 10000 ki te 100, ka 10100.

$$10100+8=3p^{2}-190+11$$

Tāpirihia te 10100 ki te 8, ka 10108.

$$10108=3p^{2}-190+11$$

Tāpirihia te -190 ki te 11, ka -179.

$$10108=3p^{2}-179$$

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

$$3p^{2}-179=10108$$

Me tāpiri te 179 ki ngā taha e rua.

$$3p^{2}=10108+179$$

Tāpirihia te 10108 ki te 179, ka 10287.

$$3p^{2}=10287$$

Whakawehea ngā taha e rua ki te 3.

$$p^{2}=\frac{10287}{3}$$

Whakawehea te 10287 ki te 3, kia riro ko 3429.

$$p^{2}=3429$$

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

$$p=3\sqrt{381} p=-3\sqrt{381}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$10000+100+8=3p^{2}-190+11$$

Tāpirihia te 10000 ki te 100, ka 10100.

$$10100+8=3p^{2}-190+11$$

Tāpirihia te 10100 ki te 8, ka 10108.

$$10108=3p^{2}-190+11$$

Tāpirihia te -190 ki te 11, ka -179.

$$10108=3p^{2}-179$$

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

$$3p^{2}-179=10108$$

Tangohia te 10108 mai i ngā taha e rua.

$$3p^{2}-179-10108=0$$

Tangohia te 10108 i te -179, ka -10287.

$$3p^{2}-10287=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -10287 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 3\left(-10287\right)}}{2\times 3}$$

Pūrua 0.

$$p=\frac{0±\sqrt{-4\times 3\left(-10287\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$p=\frac{0±\sqrt{-12\left(-10287\right)}}{2\times 3}$$

Whakareatia -12 ki te -10287.

$$p=\frac{0±\sqrt{123444}}{2\times 3}$$

Tuhia te pūtakerua o te 123444.

$$p=\frac{0±18\sqrt{381}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$p=\frac{0±18\sqrt{381}}{6}$$

Nā, me whakaoti te whārite p=\frac{0±18\sqrt{381}}{6} ina he tāpiri te ±.

$$p=3\sqrt{381}$$

Nā, me whakaoti te whārite p=\frac{0±18\sqrt{381}}{6} ina he tango te ±.

$$p=-3\sqrt{381}$$

Kua oti te whārite te whakatau.

$$p=3\sqrt{381} p=-3\sqrt{381}$$