y=5pi^3/17-sqrt{2x} eching

$$y = \frac { 5 \pi ^ { 3 } } { 17 } - \sqrt { 2 x }$$

x uchun yechish

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$y\leq \frac{5\pi ^{3}}{17}$$

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{5\pi ^{3}}{17}-\sqrt{2x}=y$$

Ikkala tarafdan \frac{5\pi ^{3}}{17} ni ayirish.

$$-\sqrt{2x}=y-\frac{5\pi ^{3}}{17}$$

Tenglamaning ikkala tarafini 17 ga ko'paytirish.

$$-17\sqrt{2x}=17y-5\pi ^{3}$$

Ikki tarafini -17 ga bo‘ling.

$$\frac{-17\sqrt{2x}}{-17}=\frac{17y-5\pi ^{3}}{-17}$$

-17 ga bo'lish -17 ga ko'paytirishni bekor qiladi.

$$\sqrt{2x}=\frac{17y-5\pi ^{3}}{-17}$$

17y-5\pi ^{3} ni -17 ga bo'lish.

$$\sqrt{2x}=-y+\frac{5\pi ^{3}}{17}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$2x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{289}$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x}{2}=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

\frac{\left(-17y+5\pi ^{3}\right)^{2}}{289} ni 2 ga bo'lish.

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

x uchun yechish (complex solution)

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$arg(-\frac{y}{2}+\frac{5\pi ^{3}}{34})<\pi \text{ or }y=\frac{5\pi ^{3}}{17}$$

y uchun yechish (complex solution)

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

y uchun yechish

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

$$x\geq 0$$