fi=ni/Nquadfjn/N eching

$$f i = \frac { n i } { N } \quad f j \frac { n } { N }$$

f uchun yechish

$$\left\{\begin{matrix}f=0\text{, }&N\neq 0\\f\in \mathrm{C}\text{, }&\left(n=-j^{-\frac{1}{2}}N\text{ or }n=j^{-\frac{1}{2}}N\right)\text{ and }j\neq 0\text{ and }N\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini N ga ko'paytirish.

$$fiN=nifj\times \frac{n}{N}$$

n\times \frac{n}{N} ni yagona kasrga aylantiring.

$$fiN=\frac{nn}{N}ifj$$

n^{2} hosil qilish uchun n va n ni ko'paytirish.

$$fiN=\frac{n^{2}}{N}ifj$$

\frac{n^{2}}{N}f ni yagona kasrga aylantiring.

$$fiN=\frac{n^{2}f}{N}ij$$

\frac{n^{2}f}{N}j ni yagona kasrga aylantiring.

$$fiN=\frac{n^{2}fj}{N}i$$

Ikkala tarafdan \frac{n^{2}fj}{N}i ni ayirish.

$$fiN-\frac{n^{2}fj}{N}i=0$$

Tenglamaning ikkala tarafini N ga ko'paytirish.

$$fiNN-n^{2}fji=0$$

Shartlarni qayta saralash.

$$iNNf-ifjn^{2}=0$$

N^{2} hosil qilish uchun N va N ni ko'paytirish.

$$iN^{2}f-ifjn^{2}=0$$

f'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(iN^{2}-ijn^{2}\right)f=0$$

0 ni iN^{2}-ijn^{2} ga bo'lish.

$$f=0$$

N uchun yechish

$$\left\{\begin{matrix}N=-\sqrt{j}n\text{; }N=\sqrt{j}n\text{, }&j\neq 0\text{ and }n\neq 0\\N\neq 0\text{, }&f=0\end{matrix}\right,$$