A/x^2+B/y^2=9 eching

$$\frac { A } { x ^ { 2 } } + \frac { B } { y ^ { 2 } } = 9$$

A uchun yechish

$$A=-\left(\frac{x}{y}\right)^{2}\left(B-9y^{2}\right)$$

$$x\neq 0\text{ and }y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x^{2}y^{2} ga, x^{2},y^{2} ning eng kichik karralisiga ko‘paytiring.

$$y^{2}A+x^{2}B=9x^{2}y^{2}$$

Ikkala tarafdan x^{2}B ni ayirish.

$$y^{2}A=9x^{2}y^{2}-x^{2}B$$

Shartlarni qayta saralash.

$$Ay^{2}=9x^{2}y^{2}-Bx^{2}$$

Tenglama standart shaklda.

$$y^{2}A=9x^{2}y^{2}-Bx^{2}$$

Ikki tarafini y^{2} ga bo‘ling.

$$\frac{y^{2}A}{y^{2}}=\frac{x^{2}\left(9y^{2}-B\right)}{y^{2}}$$

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

$$A=\frac{x^{2}\left(9y^{2}-B\right)}{y^{2}}$$

B uchun yechish

$$B=-\left(\frac{y}{x}\right)^{2}\left(A-9x^{2}\right)$$

$$x\neq 0\text{ and }y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x^{2}y^{2} ga, x^{2},y^{2} ning eng kichik karralisiga ko‘paytiring.

$$y^{2}A+x^{2}B=9x^{2}y^{2}$$

Ikkala tarafdan y^{2}A ni ayirish.

$$x^{2}B=9x^{2}y^{2}-y^{2}A$$

Shartlarni qayta saralash.

$$Bx^{2}=9x^{2}y^{2}-Ay^{2}$$

Tenglama standart shaklda.

$$x^{2}B=9x^{2}y^{2}-Ay^{2}$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}B}{x^{2}}=\frac{y^{2}\left(9x^{2}-A\right)}{x^{2}}$$

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

$$B=\frac{y^{2}\left(9x^{2}-A\right)}{x^{2}}$$