Whakaoti i te (12/10+x)*(12/10-x)=1.08

$$( \frac { 12 } { 10 } + x ) \times ( \frac { 12 } { 10 } - x ) = 1.08$$

Whakaoti mō x

$$x=0.6$$

$$x=-0.6$$

Ngā Upane mā te Kimi Pūtakerua

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\left(\frac{6}{5}+x\right)\left(\frac{12}{10}-x\right)=1.08$$

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\left(\frac{6}{5}+x\right)\left(\frac{6}{5}-x\right)=1.08$$

Whakaarohia te \left(\frac{6}{5}+x\right)\left(\frac{6}{5}-x\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 \frac{6}{5}.

$$\frac{36}{25}-x^{2}=1.08$$

Tangohia te \frac{36}{25} mai i ngā taha e rua.

$$-x^{2}=1.08-\frac{36}{25}$$

Tangohia te \frac{36}{25} i te 1.08, ka -\frac{9}{25}.

$$-x^{2}=-\frac{9}{25}$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=\frac{-\frac{9}{25}}{-1}$$

Tuhia te \frac{-\frac{9}{25}}{-1} hei hautanga kotahi.

$$x^{2}=\frac{-9}{25\left(-1\right)}$$

Whakareatia te 25 ki te -1, ka -25.

$$x^{2}=\frac{-9}{-25}$$

Ka taea te hautanga \frac{-9}{-25} te whakamāmā ki te \frac{9}{25} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=\frac{9}{25}$$

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

$$x=\frac{3}{5} x=-\frac{3}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\left(\frac{6}{5}+x\right)\left(\frac{12}{10}-x\right)=1.08$$

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\left(\frac{6}{5}+x\right)\left(\frac{6}{5}-x\right)=1.08$$

Whakaarohia te \left(\frac{6}{5}+x\right)\left(\frac{6}{5}-x\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 \frac{6}{5}.

$$\frac{36}{25}-x^{2}=1.08$$

Tangohia te 1.08 mai i ngā taha e rua.

$$\frac{36}{25}-x^{2}-1.08=0$$

Tangohia te 1.08 i te \frac{36}{25}, ka \frac{9}{25}.

$$\frac{9}{25}-x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-x^{2}+\frac{9}{25}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me \frac{9}{25} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times \frac{9}{25}}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times \frac{9}{25}}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\times \frac{9}{25}}}{2\left(-1\right)}$$

Whakareatia 4 ki te \frac{9}{25}.

$$x=\frac{0±\sqrt{\frac{36}{25}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \frac{36}{25}.

$$x=\frac{0±\frac{6}{5}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±\frac{6}{5}}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{6}{5}}{-2} ina he tāpiri te ±.

$$x=-\frac{3}{5}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{6}{5}}{-2} ina he tango te ±.

$$x=\frac{3}{5}$$

Kua oti te whārite te whakatau.

$$x=-\frac{3}{5} x=\frac{3}{5}$$