Réitigh frac{2+sqrt{5}}{2-sqrt{5}}

$$\frac { 2 + \sqrt { 5 } } { 2 - \sqrt { 5 } }$$

Luacháil

$$-4\sqrt{5}-9\approx -17.94427191$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 2+\sqrt{5} chun ainmneoir \frac{2+\sqrt{5}}{2-\sqrt{5}} a thiontú in uimhir chóimheasta.

$$\frac{\left(2+\sqrt{5}\right)\left(2+\sqrt{5}\right)}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}$$

Mar shampla \left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(2+\sqrt{5}\right)\left(2+\sqrt{5}\right)}{2^{2}-\left(\sqrt{5}\right)^{2}}$$

Cearnóg 2. Cearnóg \sqrt{5}.

$$\frac{\left(2+\sqrt{5}\right)\left(2+\sqrt{5}\right)}{4-5}$$

Dealaigh 5 ó 4 chun -1 a fháil.

$$\frac{\left(2+\sqrt{5}\right)\left(2+\sqrt{5}\right)}{-1}$$

Méadaigh 2+\sqrt{5} agus 2+\sqrt{5} chun \left(2+\sqrt{5}\right)^{2} a fháil.

$$\frac{\left(2+\sqrt{5}\right)^{2}}{-1}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(2+\sqrt{5}\right)^{2} a leathnú.

$$\frac{4+4\sqrt{5}+\left(\sqrt{5}\right)^{2}}{-1}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$\frac{4+4\sqrt{5}+5}{-1}$$

Suimigh 4 agus 5 chun 9 a fháil.

$$\frac{9+4\sqrt{5}}{-1}$$

Aon rud a roinntear ar -1, tugann sé a mhalairt. Chun an mhalairt ar 9+4\sqrt{5} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$-9-4\sqrt{5}$$