Whakaoti i te 3x^2-8=7

$$3 x ^ { 2 } - 8 = 7$$

Whakaoti mō x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 8 ki ngā taha e rua.

$$3x^{2}=7+8$$

Tāpirihia te 7 ki te 8, ka 15.

$$3x^{2}=15$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{15}{3}$$

Whakawehea te 15 ki te 3, kia riro ko 5.

$$x^{2}=5$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7 mai i ngā taha e rua.

$$3x^{2}-8-7=0$$

Tangohia te 7 i te -8, ka -15.

$$3x^{2}-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-15\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-15\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-15\right)}}{2\times 3}$$

Whakareatia -12 ki te -15.

$$x=\frac{0±\sqrt{180}}{2\times 3}$$

Tuhia te pūtakerua o te 180.

$$x=\frac{0±6\sqrt{5}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±6\sqrt{5}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{5}}{6} ina he tāpiri te ±.

$$x=\sqrt{5}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{5}}{6} ina he tango te ±.

$$x=-\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{5} x=-\sqrt{5}$$