Réitigh frac{sqrt{3}-1}{sqrt{3}+1}=a+bsqrt{3}

$$\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } = a + b \sqrt { 3 }$$

Réitigh do b.

$$b=-\frac{\sqrt{3}\left(a+\sqrt{3}-2\right)}{3}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3}-1 chun ainmneoir \frac{\sqrt{3}-1}{\sqrt{3}+1} a thiontú in uimhir chóimheasta.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}=a+b\sqrt{3}$$

Mar shampla \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\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}.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}=a+b\sqrt{3}$$

Cearnóg \sqrt{3}. Cearnóg 1.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{3-1}=a+b\sqrt{3}$$

Dealaigh 1 ó 3 chun 2 a fháil.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{2}=a+b\sqrt{3}$$

Méadaigh \sqrt{3}-1 agus \sqrt{3}-1 chun \left(\sqrt{3}-1\right)^{2} a fháil.

$$\frac{\left(\sqrt{3}-1\right)^{2}}{2}=a+b\sqrt{3}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{3}-1\right)^{2} a leathnú.

$$\frac{\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1}{2}=a+b\sqrt{3}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{3-2\sqrt{3}+1}{2}=a+b\sqrt{3}$$

Suimigh 3 agus 1 chun 4 a fháil.

$$\frac{4-2\sqrt{3}}{2}=a+b\sqrt{3}$$

Roinn 4-2\sqrt{3} faoi 2 chun 2-\sqrt{3} a fháil.

$$2-\sqrt{3}=a+b\sqrt{3}$$

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

$$a+b\sqrt{3}=2-\sqrt{3}$$

Bain a ón dá thaobh.

$$b\sqrt{3}=2-\sqrt{3}-a$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\sqrt{3}b=-a+2-\sqrt{3}$$

Roinn an dá thaobh faoi \sqrt{3}.

$$\frac{\sqrt{3}b}{\sqrt{3}}=\frac{-a+2-\sqrt{3}}{\sqrt{3}}$$

Má roinntear é faoi \sqrt{3} cuirtear an iolrúchán faoi \sqrt{3} ar ceal.

$$b=\frac{-a+2-\sqrt{3}}{\sqrt{3}}$$

Roinn -\sqrt{3}-a+2 faoi \sqrt{3}.

$$b=\frac{\sqrt{3}\left(-a+2-\sqrt{3}\right)}{3}$$

Réitigh do a.

$$a=-\sqrt{3}b+2-\sqrt{3}$$