xy^2+2xy-10x-1=0 eching

$$x y ^ { 2 } + 2 x y - 10 x - 1 = 0$$

x uchun yechish (complex solution)

$$x=\frac{1}{y^{2}+2y-10}$$

$$y\neq \sqrt{11}-1\text{ and }y\neq -\left(\sqrt{11}+1\right)$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$xy^{2}+2xy-10x=1$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y^{2}+2y-10\right)x=1$$

Ikki tarafini y^{2}+2y-10 ga bo‘ling.

$$\frac{\left(y^{2}+2y-10\right)x}{y^{2}+2y-10}=\frac{1}{y^{2}+2y-10}$$

y^{2}+2y-10 ga bo'lish y^{2}+2y-10 ga ko'paytirishni bekor qiladi.

$$x=\frac{1}{y^{2}+2y-10}$$

x uchun yechish

$$x=\frac{1}{y^{2}+2y-10}$$

$$y\neq \sqrt{11}-1\text{ and }y\neq -\sqrt{11}-1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$xy^{2}+2xy-10x=1$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y^{2}+2y-10\right)x=1$$

Ikki tarafini y^{2}+2y-10 ga bo‘ling.

$$\frac{\left(y^{2}+2y-10\right)x}{y^{2}+2y-10}=\frac{1}{y^{2}+2y-10}$$

y^{2}+2y-10 ga bo'lish y^{2}+2y-10 ga ko'paytirishni bekor qiladi.

$$x=\frac{1}{y^{2}+2y-10}$$

y uchun yechish (complex solution)

$$y=\frac{\sqrt{11x^{2}+x}}{x}-1$$

$$y=-\frac{\sqrt{11x^{2}+x}}{x}-1\text{, }x\neq 0$$

y uchun yechish

$$y=\frac{\sqrt{11x^{2}+x}}{x}-1$$

$$y=-\frac{\sqrt{11x^{2}+x}}{x}-1\text{, }x>0\text{ or }x\leq -\frac{1}{11}$$