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

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

Datrys ar gyfer t

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

Camau ar gyfer Datrys Hafaliad Llinol

I luosi \sqrt{2} a \sqrt{3}, dylid lluosi'r rhifau dan yr ail isradd.

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

Mae'n rhesymoli enwadur \frac{\sqrt{6}}{\sqrt{6}t} drwy luosi'r rhifiadur a'r enwadur â \sqrt{6}.

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

Sgwâr \sqrt{6} yw 6.

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

Lluosi \sqrt{6} a \sqrt{6} i gael 6.

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

Ystyriwch \left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Sgwâr \sqrt{2}. Sgwâr \sqrt{3}.

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

Tynnu 3 o 2 i gael -1.

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

Mae unrhyw beth sy'n cael ei rannu â -1 yn rhoi'r gwrthwyneb.

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

Defnyddio’r briodwedd ddosbarthu i luosi \sqrt{6} â \sqrt{2}-\sqrt{3}.

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

Ffactora 6=2\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{2\times 3} fel lluoswm ail israddau \sqrt{2}\sqrt{3}.

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

Lluosi \sqrt{2} a \sqrt{2} i gael 2.

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

Ffactora 6=3\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3\times 2} fel lluoswm ail israddau \sqrt{3}\sqrt{2}.

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

Lluosi \sqrt{3} a \sqrt{3} i gael 3.

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

I ddod o hyd i wrthwyneb 2\sqrt{3}-3\sqrt{2}, dewch o hyd i wrthwyneb pob term.

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

All y newidyn t ddim fod yn hafal i 0 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â 6t.

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

Aildrefnu'r termau.

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

Gwnewch y gwaith lluosi.

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

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

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

Cyfuno pob term sy'n cynnwys t.

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

Rhannu’r ddwy ochr â 18\sqrt{2}-12\sqrt{3}.

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

Mae rhannu â 18\sqrt{2}-12\sqrt{3} yn dad-wneud lluosi â 18\sqrt{2}-12\sqrt{3}.

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

Rhannwch 6 â 18\sqrt{2}-12\sqrt{3}.

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