Issolvi alpha^2+beta^2=(alpha+beta)^2-2

$$\alpha ^ { 2 } + \beta ^ { 2 } = ( \alpha + \beta ) ^ { 2 } - 2$$

Solvi għal α

$$\alpha =\frac{1}{\beta }$$

$$\beta \neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\alpha +\beta \right)^{2}.

$$\alpha ^{2}+\beta ^{2}=\alpha ^{2}+2\alpha \beta +\beta ^{2}-2$$

Naqqas \alpha ^{2} miż-żewġ naħat.

$$\alpha ^{2}+\beta ^{2}-\alpha ^{2}=2\alpha \beta +\beta ^{2}-2$$

Ikkombina \alpha ^{2} u -\alpha ^{2} biex tikseb 0.

$$\beta ^{2}=2\alpha \beta +\beta ^{2}-2$$

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

$$2\alpha \beta +\beta ^{2}-2=\beta ^{2}$$

Naqqas \beta ^{2} miż-żewġ naħat.

$$2\alpha \beta -2=\beta ^{2}-\beta ^{2}$$

Ikkombina \beta ^{2} u -\beta ^{2} biex tikseb 0.

$$2\alpha \beta -2=0$$

Żid 2 maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$2\alpha \beta =2$$

L-ekwazzjoni hija f'forma standard.

$$2\beta \alpha =2$$

Iddividi ż-żewġ naħat b'2\beta .

$$\frac{2\beta \alpha }{2\beta }=\frac{2}{2\beta }$$

Meta tiddividi b'2\beta titneħħa l-multiplikazzjoni b'2\beta .

$$\alpha =\frac{2}{2\beta }$$

Iddividi 2 b'2\beta .

$$\alpha =\frac{1}{\beta }$$

Solvi għal β

$$\beta =\frac{1}{\alpha }$$

$$\alpha \neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\alpha +\beta \right)^{2}.

$$\alpha ^{2}+\beta ^{2}=\alpha ^{2}+2\alpha \beta +\beta ^{2}-2$$

Naqqas 2\alpha \beta miż-żewġ naħat.

$$\alpha ^{2}+\beta ^{2}-2\alpha \beta =\alpha ^{2}+\beta ^{2}-2$$

Naqqas \beta ^{2} miż-żewġ naħat.

$$\alpha ^{2}+\beta ^{2}-2\alpha \beta -\beta ^{2}=\alpha ^{2}-2$$

Ikkombina \beta ^{2} u -\beta ^{2} biex tikseb 0.

$$\alpha ^{2}-2\alpha \beta =\alpha ^{2}-2$$

Naqqas \alpha ^{2} miż-żewġ naħat.

$$-2\alpha \beta =\alpha ^{2}-2-\alpha ^{2}$$

Ikkombina \alpha ^{2} u -\alpha ^{2} biex tikseb 0.

$$-2\alpha \beta =-2$$

L-ekwazzjoni hija f'forma standard.

$$\left(-2\alpha \right)\beta =-2$$

Iddividi ż-żewġ naħat b'-2\alpha .

$$\frac{\left(-2\alpha \right)\beta }{-2\alpha }=-\frac{2}{-2\alpha }$$

Meta tiddividi b'-2\alpha titneħħa l-multiplikazzjoni b'-2\alpha .

$$\beta =-\frac{2}{-2\alpha }$$

Iddividi -2 b'-2\alpha .

$$\beta =\frac{1}{\alpha }$$