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

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

Solvi għal t

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{6}}{\sqrt{6}t} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

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

Il-kwadrat ta' \sqrt{6} huwa 6.

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

Immultiplika \sqrt{6} u \sqrt{6} biex tikseb 6.

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

Ikkunsidra li \left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra \sqrt{2}. Ikkwadra \sqrt{3}.

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

Naqqas 3 minn 2 biex tikseb -1.

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

Kwalunkwe ħaġa diviża b '-1 jagħtik oppost tiegħu.

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

Uża l-propjetà distributtiva biex timmultiplika \sqrt{6} b'\sqrt{2}-\sqrt{3}.

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

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

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

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

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

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

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

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

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

Biex issib l-oppost ta' 2\sqrt{3}-3\sqrt{2}, sib l-oppost ta' kull terminu.

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

Il-varjabbli t ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'6t.

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

Erġa' ordna t-termini.

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

Agħmel il-multiplikazzjonijiet.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Ikkombina t-termini kollha li fihom t.

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

Iddividi ż-żewġ naħat b'18\sqrt{2}-12\sqrt{3}.

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

Meta tiddividi b'18\sqrt{2}-12\sqrt{3} titneħħa l-multiplikazzjoni b'18\sqrt{2}-12\sqrt{3}.

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

Iddividi 6 b'18\sqrt{2}-12\sqrt{3}.

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