Whakaoti i te 6sqrt{2}-6+12/10+6sqrt{2}

$$6 \sqrt { 2 } - 6 + \frac { 12 } { 10 + 6 \sqrt { 2 } }$$

Aromātai

$$\frac{24\sqrt{2}-12}{7}\approx 3.1344465$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{12}{10+6\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 10-6\sqrt{2}.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{\left(10+6\sqrt{2}\right)\left(10-6\sqrt{2}\right)}$$

Whakaarohia te \left(10+6\sqrt{2}\right)\left(10-6\sqrt{2}\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}.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{10^{2}-\left(6\sqrt{2}\right)^{2}}$$

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-\left(6\sqrt{2}\right)^{2}}$$

Whakarohaina te \left(6\sqrt{2}\right)^{2}.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-6^{2}\left(\sqrt{2}\right)^{2}}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-36\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-36\times 2}$$

Whakareatia te 36 ki te 2, ka 72.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{100-72}$$

Tangohia te 72 i te 100, ka 28.

$$6\sqrt{2}-6+\frac{12\left(10-6\sqrt{2}\right)}{28}$$

Whakawehea te 12\left(10-6\sqrt{2}\right) ki te 28, kia riro ko \frac{3}{7}\left(10-6\sqrt{2}\right).

$$6\sqrt{2}-6+\frac{3}{7}\left(10-6\sqrt{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{7} ki te 10-6\sqrt{2}.

$$6\sqrt{2}-6+\frac{3}{7}\times 10+\frac{3}{7}\left(-6\right)\sqrt{2}$$

Tuhia te \frac{3}{7}\times 10 hei hautanga kotahi.

$$6\sqrt{2}-6+\frac{3\times 10}{7}+\frac{3}{7}\left(-6\right)\sqrt{2}$$

Whakareatia te 3 ki te 10, ka 30.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{3}{7}\left(-6\right)\sqrt{2}$$

Tuhia te \frac{3}{7}\left(-6\right) hei hautanga kotahi.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{3\left(-6\right)}{7}\sqrt{2}$$

Whakareatia te 3 ki te -6, ka -18.

$$6\sqrt{2}-6+\frac{30}{7}+\frac{-18}{7}\sqrt{2}$$

Ka taea te hautanga \frac{-18}{7} te tuhi anō ko -\frac{18}{7} mā te tango i te tohu tōraro.

$$6\sqrt{2}-6+\frac{30}{7}-\frac{18}{7}\sqrt{2}$$

Me tahuri te -6 ki te hautau -\frac{42}{7}.

$$6\sqrt{2}-\frac{42}{7}+\frac{30}{7}-\frac{18}{7}\sqrt{2}$$

Tā te mea he rite te tauraro o -\frac{42}{7} me \frac{30}{7}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$6\sqrt{2}+\frac{-42+30}{7}-\frac{18}{7}\sqrt{2}$$

Tāpirihia te -42 ki te 30, ka -12.

$$6\sqrt{2}-\frac{12}{7}-\frac{18}{7}\sqrt{2}$$

Pahekotia te 6\sqrt{2} me -\frac{18}{7}\sqrt{2}, ka \frac{24}{7}\sqrt{2}.

$$\frac{24}{7}\sqrt{2}-\frac{12}{7}$$

Tauwehe

$$\frac{12 {(2 \sqrt{2} - 1)}}{7} = 3.134446499564898$$