2x^2=i-xy^2zj+3yz^2k eching

$$2 x ^ { 2 } = i - x y ^ { 2 } z j + 3 y z ^ { 2 } k$$

j uchun yechish

$$\left\{\begin{matrix}j=\frac{i+3kyz^{2}-2x^{2}}{xzy^{2}}\text{, }&z\neq 0\text{ and }y\neq 0\text{ and }x\neq 0\\j\in \mathrm{C}\text{, }&\left(x=0\text{ and }y=\frac{-i}{3kz^{2}}\text{ and }k\neq 0\text{ and }z\neq 0\right)\text{ or }\left(x=\frac{1}{2}+\frac{1}{2}i\text{ and }y=0\right)\text{ or }\left(x=\frac{1}{2}+\frac{1}{2}i\text{ and }z=0\right)\text{ or }\left(x=-\frac{1}{2}-\frac{1}{2}i\text{ and }y=0\right)\text{ or }\left(x=-\frac{1}{2}-\frac{1}{2}i\text{ and }z=0\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$i-xy^{2}zj+3yz^{2}k=2x^{2}$$

Ikkala tarafdan 3yz^{2}k ni ayirish.

$$i-xy^{2}zj=2x^{2}-3yz^{2}k$$

Ikkala tarafdan i ni ayirish.

$$-xy^{2}zj=2x^{2}-3yz^{2}k-i$$

Tenglama standart shaklda.

$$\left(-xzy^{2}\right)j=2x^{2}-3kyz^{2}-i$$

Ikki tarafini -xy^{2}z ga bo‘ling.

$$\frac{\left(-xzy^{2}\right)j}{-xzy^{2}}=\frac{2x^{2}-3kyz^{2}-i}{-xzy^{2}}$$

-xy^{2}z ga bo'lish -xy^{2}z ga ko'paytirishni bekor qiladi.

$$j=\frac{2x^{2}-3kyz^{2}-i}{-xzy^{2}}$$

-i+2x^{2}-3yz^{2}k ni -xy^{2}z ga bo'lish.

$$j=-\frac{2x^{2}-3kyz^{2}-i}{xzy^{2}}$$

k uchun yechish

$$\left\{\begin{matrix}k=-\frac{i-jxzy^{2}-2x^{2}}{3yz^{2}}\text{, }&z\neq 0\text{ and }y\neq 0\\k\in \mathrm{C}\text{, }&\left(x=\frac{1}{2}+\frac{1}{2}i\text{ and }y=0\right)\text{ or }\left(x=\frac{1}{2}+\frac{1}{2}i\text{ and }z=0\right)\text{ or }\left(x=-\frac{1}{2}-\frac{1}{2}i\text{ and }y=0\right)\text{ or }\left(x=-\frac{1}{2}-\frac{1}{2}i\text{ and }z=0\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$i-xy^{2}zj+3yz^{2}k=2x^{2}$$

Ikkala tarafdan i-xy^{2}zj ni ayirish.

$$3yz^{2}k=2x^{2}-\left(i-xy^{2}zj\right)$$

i-xy^{2}zj teskarisini topish uchun har birining teskarisini toping.

$$3yz^{2}k=2x^{2}-i+xy^{2}zj$$

Tenglama standart shaklda.

$$3yz^{2}k=2x^{2}+jxzy^{2}-i$$

Ikki tarafini 3yz^{2} ga bo‘ling.

$$\frac{3yz^{2}k}{3yz^{2}}=\frac{2x^{2}+jxzy^{2}-i}{3yz^{2}}$$

3yz^{2} ga bo'lish 3yz^{2} ga ko'paytirishni bekor qiladi.

$$k=\frac{2x^{2}+jxzy^{2}-i}{3yz^{2}}$$