Whakaoti i te sqrt{2}+1-frac{1+sqrt{2}}{sqrt{2}+156}

$$\sqrt{ 2 } +1- \frac{ 1+ \sqrt{ 2 } }{ \sqrt{ 2 } +156 }$$

Aromātai

$$\frac{24179\sqrt{2}}{24334}+\frac{12090}{12167}\approx 2.398876869$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{1+\sqrt{2}}{\sqrt{2}+156} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}-156.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}+156\right)\left(\sqrt{2}-156\right)}$$

Whakaarohia te \left(\sqrt{2}+156\right)\left(\sqrt{2}-156\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}.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}\right)^{2}-156^{2}}$$

Pūrua \sqrt{2}. Pūrua 156.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{2-24336}$$

Tangohia te 24336 i te 2, ka -24334.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{-24334}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 1+\sqrt{2} ki ia tau o \sqrt{2}-156.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+\left(\sqrt{2}\right)^{2}-156\sqrt{2}}{-24334}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+2-156\sqrt{2}}{-24334}$$

Tāpirihia te -156 ki te 2, ka -154.

$$\sqrt{2}+1-\frac{\sqrt{2}-154-156\sqrt{2}}{-24334}$$

Pahekotia te \sqrt{2} me -156\sqrt{2}, ka -155\sqrt{2}.

$$\sqrt{2}+1-\frac{-155\sqrt{2}-154}{-24334}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\sqrt{2}+1-\frac{155\sqrt{2}+154}{24334}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia \sqrt{2}+1 ki te \frac{24334}{24334}.

$$\frac{24334\left(\sqrt{2}+1\right)}{24334}-\frac{155\sqrt{2}+154}{24334}$$

Tā te mea he rite te tauraro o \frac{24334\left(\sqrt{2}+1\right)}{24334} me \frac{155\sqrt{2}+154}{24334}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right)}{24334}$$

Mahia ngā whakarea i roto o 24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right).

$$\frac{24334\sqrt{2}[phone]\sqrt{2}-154}{24334}$$

Mahia ngā tātaitai i roto o 24334\sqrt{2}[phone]\sqrt{2}-154.

$$\frac{24179\sqrt{2}+24180}{24334}$$