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

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

Solvi għal b

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Iddividi 2 b'\frac{\sqrt{2}}{2} billi timmultiplika 2 bir-reċiproku ta' \frac{\sqrt{2}}{2}.

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

Immultiplika 2 u 2 biex tikseb 4.

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

Irrazzjonalizza d-denominatur tal-\frac{4}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Iddividi 4\sqrt{2} b'2 biex tikseb2\sqrt{2}.

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

Iddividi b b'\frac{\sqrt{2}+\sqrt{6}}{4} billi timmultiplika b bir-reċiproku ta' \frac{\sqrt{2}+\sqrt{6}}{4}.

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

Irrazzjonalizza d-denominatur tal-\frac{b\times 4}{\sqrt{2}+\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}-\sqrt{6}.

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

Ikkunsidra li \left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\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}.

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

Ikkwadra \sqrt{2}. Ikkwadra \sqrt{6}.

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

Naqqas 6 minn 2 biex tikseb -4.

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

Annulla -4 u -4.

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

Uża l-propjetà distributtiva biex timmultiplika b\left(-1\right) b'\sqrt{2}-\sqrt{6}.

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

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

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

Ikkombina t-termini kollha li fihom b.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-\sqrt{2}+\sqrt{6}.

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

Meta tiddividi b'-\sqrt{2}+\sqrt{6} titneħħa l-multiplikazzjoni b'-\sqrt{2}+\sqrt{6}.

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

Iddividi 2\sqrt{2} b'-\sqrt{2}+\sqrt{6}.

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