25^y=100*sqrt{x}+1/y= eching

$$25 ^ { y } = 100 \cdot \sqrt { x } + \frac { 1 } { y } =$$

x uchun yechish

$$x=\frac{\left(-25^{y}+\frac{1}{y}\right)^{2}}{10000}$$

$$\left(\frac{|1-y\times 25^{y}|}{|y|}\leq 0\text{ or }-\frac{25^{y}}{100}+\frac{1}{100y}\leq 0\right)\text{ and }y\neq 0$$

Ildizli tenglamalarni yechish qadamlari

Tenglamaning ikkala tarafini y ga ko'paytirish.

$$y\times 25^{y}=100\sqrt{x}y+1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$100\sqrt{x}y+1=y\times 25^{y}$$

Ikkala tarafdan 1 ni ayirish.

$$100\sqrt{x}y=y\times 25^{y}-1$$

Ikki tarafini 100y ga bo‘ling.

$$\frac{100y\sqrt{x}}{100y}=\frac{y\times 25^{y}-1}{100y}$$

100y ga bo'lish 100y ga ko'paytirishni bekor qiladi.

$$\sqrt{x}=\frac{y\times 25^{y}-1}{100y}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x=\frac{\left(y\times 25^{y}-1\right)^{2}}{10000y^{2}}$$

x uchun yechish (complex solution)

$$x=\frac{\left(-25^{y}+\frac{1}{y}\right)^{2}}{10000}$$

$$\left(y\neq 0\text{ and }1-y\times 25^{y}=0\text{ and }\frac{1-y\times 25^{y}}{100}=0\right)\text{ or }\left(y\neq 0\text{ and }arg(-\frac{25^{y}}{100}+\frac{1}{100y})\geq \pi \text{ and }\frac{1-y\times 25^{y}}{100}\neq 0\right)$$