Whakaoti i te 4x^2-5=7

$$4 x ^ { 2 } - 5 = 7$$

Whakaoti mō x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 5 ki ngā taha e rua.

$$4x^{2}=7+5$$

Tāpirihia te 7 ki te 5, ka 12.

$$4x^{2}=12$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{12}{4}$$

Whakawehea te 12 ki te 4, kia riro ko 3.

$$x^{2}=3$$

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

$$x=\sqrt{3} x=-\sqrt{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7 mai i ngā taha e rua.

$$4x^{2}-5-7=0$$

Tangohia te 7 i te -5, ka -12.

$$4x^{2}-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-12\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-12\right)}}{2\times 4}$$

Whakareatia -16 ki te -12.

$$x=\frac{0±\sqrt{192}}{2\times 4}$$

Tuhia te pūtakerua o te 192.

$$x=\frac{0±8\sqrt{3}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±8\sqrt{3}}{8}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{3}}{8} ina he tāpiri te ±.

$$x=\sqrt{3}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{3}}{8} ina he tango te ±.

$$x=-\sqrt{3}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{3} x=-\sqrt{3}$$