y^-1=x^3+1/2 eching

$${ y }^{ -1 } = \frac{ { x }^{ 3 } +1 }{ 2 }$$

y uchun yechish (complex solution)

$$y=\frac{2}{x^{3}+1}$$

$$x\neq -1\text{ and }x\neq \frac{-\sqrt{3}i+1}{2}\text{ and }x\neq \frac{1+\sqrt{3}i}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2y^{-1}=x^{3}+1$$

Shartlarni qayta saralash.

$$2\times \frac{1}{y}=x^{3}+1$$

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$2\times 1=yx^{3}+y$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$2=yx^{3}+y$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$yx^{3}+y=2$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{3}+1\right)y=2$$

Ikki tarafini x^{3}+1 ga bo‘ling.

$$\frac{\left(x^{3}+1\right)y}{x^{3}+1}=\frac{2}{x^{3}+1}$$

x^{3}+1 ga bo'lish x^{3}+1 ga ko'paytirishni bekor qiladi.

$$y=\frac{2}{x^{3}+1}$$

2 ni x^{3}+1 ga bo'lish.

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

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{2}{\left(x+1\right)\left(x^{2}-x+1\right)}\text{, }y\neq 0$$

y uchun yechish

$$y=\frac{2}{x^{3}+1}$$

$$x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2y^{-1}=x^{3}+1$$

Shartlarni qayta saralash.

$$2\times \frac{1}{y}=x^{3}+1$$

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$2\times 1=yx^{3}+y$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$2=yx^{3}+y$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$yx^{3}+y=2$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{3}+1\right)y=2$$

Ikki tarafini x^{3}+1 ga bo‘ling.

$$\frac{\left(x^{3}+1\right)y}{x^{3}+1}=\frac{2}{x^{3}+1}$$

x^{3}+1 ga bo'lish x^{3}+1 ga ko'paytirishni bekor qiladi.

$$y=\frac{2}{x^{3}+1}$$

2 ni x^{3}+1 ga bo'lish.

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

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{2}{\left(x+1\right)\left(x^{2}-x+1\right)}\text{, }y\neq 0$$

x uchun yechish (complex solution)

$$x=e^{\frac{2\pi i}{3}}\sqrt[3]{-1+\frac{2}{y}}$$

$$x=\sqrt[3]{-1+\frac{2}{y}}$$

$$x=e^{\frac{4\pi i}{3}}\sqrt[3]{-1+\frac{2}{y}}\text{, }y\neq 0$$

x uchun yechish

$$x=\sqrt[3]{-1+\frac{2}{y}}$$

$$y\neq 0$$