Issolvi -(lambda-1)(lambda^2-blambda+5)=0

$$- ( \lambda - 1 ) ( \lambda ^ { 2 } - b \lambda + 5 ) = 0$$

Solvi għal b (complex solution)

$$\left\{\begin{matrix}b=\lambda +\frac{5}{\lambda }\text{, }&\lambda \neq 0\\b\in \mathrm{C}\text{, }&\lambda =1\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Biex issib l-oppost ta' \lambda -1, sib l-oppost ta' kull terminu.

$$\left(-\lambda +1\right)\left(\lambda ^{2}-b\lambda +5\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika -\lambda +1 b'\lambda ^{2}-b\lambda +5.

$$-\lambda ^{3}+\lambda ^{2}b-5\lambda +\lambda ^{2}-b\lambda +5=0$$

Żid \lambda ^{3} maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$\lambda ^{2}b-5\lambda +\lambda ^{2}-b\lambda +5=\lambda ^{3}$$

Żid 5\lambda maż-żewġ naħat.

$$\lambda ^{2}b+\lambda ^{2}-b\lambda +5=\lambda ^{3}+5\lambda$$

Naqqas \lambda ^{2} miż-żewġ naħat.

$$\lambda ^{2}b-b\lambda +5=\lambda ^{3}+5\lambda -\lambda ^{2}$$

Naqqas 5 miż-żewġ naħat.

$$\lambda ^{2}b-b\lambda =\lambda ^{3}+5\lambda -\lambda ^{2}-5$$

Ikkombina t-termini kollha li fihom b.

$$\left(\lambda ^{2}-\lambda \right)b=\lambda ^{3}+5\lambda -\lambda ^{2}-5$$

L-ekwazzjoni hija f'forma standard.

$$\left(\lambda ^{2}-\lambda \right)b=\lambda ^{3}-\lambda ^{2}+5\lambda -5$$

Iddividi ż-żewġ naħat b'\lambda ^{2}-\lambda .

$$\frac{\left(\lambda ^{2}-\lambda \right)b}{\lambda ^{2}-\lambda }=\frac{\left(\lambda -1\right)\left(\lambda ^{2}+5\right)}{\lambda ^{2}-\lambda }$$

Meta tiddividi b'\lambda ^{2}-\lambda titneħħa l-multiplikazzjoni b'\lambda ^{2}-\lambda .

$$b=\frac{\left(\lambda -1\right)\left(\lambda ^{2}+5\right)}{\lambda ^{2}-\lambda }$$

Iddividi \left(-1+\lambda \right)\left(5+\lambda ^{2}\right) b'\lambda ^{2}-\lambda .

$$b=\lambda +\frac{5}{\lambda }$$

Solvi għal b

$$\left\{\begin{matrix}b=\lambda +\frac{5}{\lambda }\text{, }&\lambda \neq 0\\b\in \mathrm{R}\text{, }&\lambda =1\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Biex issib l-oppost ta' \lambda -1, sib l-oppost ta' kull terminu.

$$\left(-\lambda +1\right)\left(\lambda ^{2}-b\lambda +5\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika -\lambda +1 b'\lambda ^{2}-b\lambda +5.

$$-\lambda ^{3}+\lambda ^{2}b-5\lambda +\lambda ^{2}-b\lambda +5=0$$

Żid \lambda ^{3} maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$\lambda ^{2}b-5\lambda +\lambda ^{2}-b\lambda +5=\lambda ^{3}$$

Żid 5\lambda maż-żewġ naħat.

$$\lambda ^{2}b+\lambda ^{2}-b\lambda +5=\lambda ^{3}+5\lambda$$

Naqqas \lambda ^{2} miż-żewġ naħat.

$$\lambda ^{2}b-b\lambda +5=\lambda ^{3}+5\lambda -\lambda ^{2}$$

Naqqas 5 miż-żewġ naħat.

$$\lambda ^{2}b-b\lambda =\lambda ^{3}+5\lambda -\lambda ^{2}-5$$

Ikkombina t-termini kollha li fihom b.

$$\left(\lambda ^{2}-\lambda \right)b=\lambda ^{3}+5\lambda -\lambda ^{2}-5$$

L-ekwazzjoni hija f'forma standard.

$$\left(\lambda ^{2}-\lambda \right)b=\lambda ^{3}-\lambda ^{2}+5\lambda -5$$

Iddividi ż-żewġ naħat b'\lambda ^{2}-\lambda .

$$\frac{\left(\lambda ^{2}-\lambda \right)b}{\lambda ^{2}-\lambda }=\frac{\left(\lambda -1\right)\left(\lambda ^{2}+5\right)}{\lambda ^{2}-\lambda }$$

Meta tiddividi b'\lambda ^{2}-\lambda titneħħa l-multiplikazzjoni b'\lambda ^{2}-\lambda .

$$b=\frac{\left(\lambda -1\right)\left(\lambda ^{2}+5\right)}{\lambda ^{2}-\lambda }$$

Iddividi \left(-1+\lambda \right)\left(5+\lambda ^{2}\right) b'\lambda ^{2}-\lambda .

$$b=\lambda +\frac{5}{\lambda }$$

Solvi għal λ (complex solution)

$$\lambda =\frac{-\sqrt{b^{2}-20}+b}{2}$$

$$\lambda =1$$

$$\lambda =\frac{\sqrt{b^{2}-20}+b}{2}$$

Solvi għal λ

$$\left\{\begin{matrix}\\\lambda =1\text{, }&\text{unconditionally}\\\lambda =\frac{\sqrt{b^{2}-20}+b}{2}\text{; }\lambda =\frac{-\sqrt{b^{2}-20}+b}{2}\text{, }&|b|\geq 2\sqrt{5}\end{matrix}\right.$$