Whakaoti i te x^2/4=x^2/9+1/9

$$\frac { x ^ { 2 } } { 4 } = \frac { x ^ { 2 } } { 9 } + \frac { 1 } { 9 }$$

Whakaoti mō x

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

$$x=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 4,9.

$$9x^{2}=4x^{2}+4$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$9x^{2}-4x^{2}=4$$

Pahekotia te 9x^{2} me -4x^{2}, ka 5x^{2}.

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

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{4}{5}$$

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

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 4,9.

$$9x^{2}=4x^{2}+4$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$9x^{2}-4x^{2}=4$$

Pahekotia te 9x^{2} me -4x^{2}, ka 5x^{2}.

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

Tangohia te 4 mai i ngā taha e rua.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-4\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-4\right)}}{2\times 5}$$

Whakareatia -20 ki te -4.

$$x=\frac{0±\sqrt{80}}{2\times 5}$$

Tuhia te pūtakerua o te 80.

$$x=\frac{0±4\sqrt{5}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±4\sqrt{5}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{5}}{10} ina he tāpiri te ±.

$$x=\frac{2\sqrt{5}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{5}}{10} ina he tango te ±.

$$x=-\frac{2\sqrt{5}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$