Whakaoti i te 7^2/x^2-49=1

$$\frac { 7 ^ { 2 } } { x ^ { 2 } - 49 } = 1$$

Whakaoti mō x

$$x=7\sqrt{2}\approx 9.899494937$$

$$x=-7\sqrt{2}\approx -9.899494937$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -7,7 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-7\right)\left(x+7\right).

$$7^{2}=\left(x-7\right)\left(x+7\right)$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49=\left(x-7\right)\left(x+7\right)$$

Whakaarohia te \left(x-7\right)\left(x+7\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 7.

$$49=x^{2}-49$$

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

$$x^{2}-49=49$$

Me tāpiri te 49 ki ngā taha e rua.

$$x^{2}=49+49$$

Tāpirihia te 49 ki te 49, ka 98.

$$x^{2}=98$$

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

$$x=7\sqrt{2} x=-7\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -7,7 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-7\right)\left(x+7\right).

$$7^{2}=\left(x-7\right)\left(x+7\right)$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49=\left(x-7\right)\left(x+7\right)$$

Whakaarohia te \left(x-7\right)\left(x+7\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 7.

$$49=x^{2}-49$$

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

$$x^{2}-49=49$$

Tangohia te 49 mai i ngā taha e rua.

$$x^{2}-49-49=0$$

Tangohia te 49 i te -49, ka -98.

$$x^{2}-98=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -98 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-98\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-98\right)}}{2}$$

Whakareatia -4 ki te -98.

$$x=\frac{0±\sqrt{392}}{2}$$

Tuhia te pūtakerua o te 392.

$$x=\frac{0±14\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±14\sqrt{2}}{2} ina he tāpiri te ±.

$$x=7\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±14\sqrt{2}}{2} ina he tango te ±.

$$x=-7\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=7\sqrt{2} x=-7\sqrt{2}$$