32y/x^2+16/x=5y eching

$$\frac { 32 y } { x ^ { 2 } } + \frac { 16 } { x } = 5 y$$

y uchun yechish (complex solution)

$$y=-\frac{16x}{32-5x^{2}}$$

$$x\neq -\frac{4\sqrt{10}}{5}\text{ and }x\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$32y+x\times 16=5yx^{2}$$

Ikkala tarafdan 5yx^{2} ni ayirish.

$$32y+x\times 16-5yx^{2}=0$$

Ikkala tarafdan x\times 16 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$32y-5yx^{2}=-x\times 16$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(32-5x^{2}\right)y=-x\times 16$$

Tenglama standart shaklda.

$$\left(32-5x^{2}\right)y=-16x$$

Ikki tarafini -5x^{2}+32 ga bo‘ling.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

-5x^{2}+32 ga bo'lish -5x^{2}+32 ga ko'paytirishni bekor qiladi.

$$y=-\frac{16x}{32-5x^{2}}$$

y uchun yechish

$$y=-\frac{16x}{32-5x^{2}}$$

$$|x|\neq \frac{4\sqrt{10}}{5}\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$32y+x\times 16=5yx^{2}$$

Ikkala tarafdan 5yx^{2} ni ayirish.

$$32y+x\times 16-5yx^{2}=0$$

Ikkala tarafdan x\times 16 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$32y-5yx^{2}=-x\times 16$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(32-5x^{2}\right)y=-x\times 16$$

Tenglama standart shaklda.

$$\left(32-5x^{2}\right)y=-16x$$

Ikki tarafini -5x^{2}+32 ga bo‘ling.

$$\frac{\left(32-5x^{2}\right)y}{32-5x^{2}}=-\frac{16x}{32-5x^{2}}$$

-5x^{2}+32 ga bo'lish -5x^{2}+32 ga ko'paytirishni bekor qiladi.

$$y=-\frac{16x}{32-5x^{2}}$$

x uchun yechish

$$x=-\frac{4\left(\sqrt{2\left(5y^{2}+2\right)}-2\right)}{5y}$$

$$x=\frac{4\sqrt{2}\left(\sqrt{5y^{2}+2}+\sqrt{2}\right)}{5y}\text{, }y\neq 0$$