Réitigh frac{sqrt{6}}{sqrt{2}tsqrt{3}}=frac{sqrt{6}(sqrt{2}-sqrt{3})}{(sqrt{2}+sqrt{3})(sqrt{2}-sqrt{3})}=

$$\frac { \sqrt { 6 } } { \sqrt { 2 } t \sqrt { 3 } } = \frac { \sqrt { 6 } ( \sqrt { 2 } - \sqrt { 3 } ) } { ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 2 } - \sqrt { 3 } ) } =$$

Réitigh do t.

$$t = \frac{2 \sqrt{3} + 3 \sqrt{2}}{6} \approx 1.28445705$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{3} a iolrú.

$$\frac{\sqrt{6}}{\sqrt{6}t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

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

$$\frac{\sqrt{6}\sqrt{6}}{\left(\sqrt{6}\right)^{2}t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

Is é 6 uimhir chearnach \sqrt{6}.

$$\frac{\sqrt{6}\sqrt{6}}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

Méadaigh \sqrt{6} agus \sqrt{6} chun 6 a fháil.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

Mar shampla \left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\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}.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

Cearnóg \sqrt{2}. Cearnóg \sqrt{3}.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}$$

Dealaigh 3 ó 2 chun -1 a fháil.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{-1}$$

Aon rud a roinntear ar -1, tugann sé a mhalairt.

$$\frac{6}{6t}=-\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)$$

Úsáid an t-airí dáileach chun \sqrt{6} a mhéadú faoi \sqrt{2}-\sqrt{3}.

$$\frac{6}{6t}=-\left(\sqrt{6}\sqrt{2}-\sqrt{6}\sqrt{3}\right)$$

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

$$\frac{6}{6t}=-\left(\sqrt{2}\sqrt{3}\sqrt{2}-\sqrt{6}\sqrt{3}\right)$$

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$\frac{6}{6t}=-\left(2\sqrt{3}-\sqrt{6}\sqrt{3}\right)$$

Fachtóirigh 6=3\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{3\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{3}\sqrt{2}.

$$\frac{6}{6t}=-\left(2\sqrt{3}-\sqrt{3}\sqrt{2}\sqrt{3}\right)$$

Méadaigh \sqrt{3} agus \sqrt{3} chun 3 a fháil.

$$\frac{6}{6t}=-\left(2\sqrt{3}-3\sqrt{2}\right)$$

Chun an mhalairt ar 2\sqrt{3}-3\sqrt{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\frac{6}{6t}=-2\sqrt{3}+3\sqrt{2}$$

Ní féidir leis an athróg t a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi 6t.

$$6=-2\sqrt{3}\times 6t+3\sqrt{2}\times 6t$$

Athordaigh na téarmaí.

$$6=3\times 6\sqrt{2}t-2\times 6\sqrt{3}t$$

Déan na hiolrúcháin.

$$6=18\sqrt{2}t-12\sqrt{3}t$$

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

$$18\sqrt{2}t-12\sqrt{3}t=6$$

Comhcheangail na téarmaí ar fad ina bhfuil t.

$$\left(18\sqrt{2}-12\sqrt{3}\right)t=6$$

Roinn an dá thaobh faoi 18\sqrt{2}-12\sqrt{3}.

$$\frac{\left(18\sqrt{2}-12\sqrt{3}\right)t}{18\sqrt{2}-12\sqrt{3}}=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

Má roinntear é faoi 18\sqrt{2}-12\sqrt{3} cuirtear an iolrúchán faoi 18\sqrt{2}-12\sqrt{3} ar ceal.

$$t=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

Roinn 6 faoi 18\sqrt{2}-12\sqrt{3}.

$$t=\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}$$