Réitigh 2/sqrt{2/2}=b/frac{sqrt{2+sqrt{6}}{4}}

$$\frac { 2 } { \frac { \sqrt { 2 } } { 2 } } = \frac { b } { \frac { \sqrt { 2 } + \sqrt { 6 } } { 4 } }$$

Réitigh do b.

$$b=\sqrt{3}+1\approx 2.732050808$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Roinn 2 faoi \frac{\sqrt{2}}{2} trí 2 a mhéadú faoi dheilín \frac{\sqrt{2}}{2}.

$$\frac{2\times 2}{\sqrt{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$\frac{4}{\sqrt{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{4}{\sqrt{2}} a thiontú in uimhir chóimheasta.

$$\frac{4\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{4\sqrt{2}}{2}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

Roinn 4\sqrt{2} faoi 2 chun 2\sqrt{2} a fháil.

$$2\sqrt{2}=\frac{b}{\frac{\sqrt{2}+\sqrt{6}}{4}}$$

Roinn b faoi \frac{\sqrt{2}+\sqrt{6}}{4} trí b a mhéadú faoi dheilín \frac{\sqrt{2}+\sqrt{6}}{4}.

$$2\sqrt{2}=\frac{b\times 4}{\sqrt{2}+\sqrt{6}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}-\sqrt{6} chun ainmneoir \frac{b\times 4}{\sqrt{2}+\sqrt{6}} a thiontú in uimhir chóimheasta.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right)}$$

Mar shampla \left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\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}.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{6}\right)^{2}}$$

Cearnóg \sqrt{2}. Cearnóg \sqrt{6}.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{2-6}$$

Dealaigh 6 ó 2 chun -4 a fháil.

$$2\sqrt{2}=\frac{b\times 4\left(\sqrt{2}-\sqrt{6}\right)}{-4}$$

Cealaigh -4 agus -4.

$$2\sqrt{2}=b\left(-1\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Úsáid an t-airí dáileach chun b\left(-1\right) a mhéadú faoi \sqrt{2}-\sqrt{6}.

$$2\sqrt{2}=-b\sqrt{2}+b\sqrt{6}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$-b\sqrt{2}+b\sqrt{6}=2\sqrt{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil b.

$$\left(-\sqrt{2}+\sqrt{6}\right)b=2\sqrt{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(\sqrt{6}-\sqrt{2}\right)b=2\sqrt{2}$$

Roinn an dá thaobh faoi -\sqrt{2}+\sqrt{6}.

$$\frac{\left(\sqrt{6}-\sqrt{2}\right)b}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{2}}{\sqrt{6}-\sqrt{2}}$$

Má roinntear é faoi -\sqrt{2}+\sqrt{6} cuirtear an iolrúchán faoi -\sqrt{2}+\sqrt{6} ar ceal.

$$b=\frac{2\sqrt{2}}{\sqrt{6}-\sqrt{2}}$$

Roinn 2\sqrt{2} faoi -\sqrt{2}+\sqrt{6}.

$$b=\sqrt{3}+1$$