1/sqrt{x}=1/2y+1/3z eching

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

y uchun yechish

$$y=-\frac{3\sqrt{x}z}{2\left(-3z+\sqrt{x}\right)}$$

$$z\neq 0\text{ and }\left(z<0\text{ or }x\neq 9z^{2}\right)\text{ and }x>0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6yz ga, 2y,3z ning eng kichik karralisiga ko‘paytiring.

$$6yzx^{-\frac{1}{2}}=3z+2y$$

Ikkala tarafdan 2y ni ayirish.

$$6yzx^{-\frac{1}{2}}-2y=3z$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(6zx^{-\frac{1}{2}}-2\right)y=3z$$

Tenglama standart shaklda.

$$\left(\frac{6z}{\sqrt{x}}-2\right)y=3z$$

Ikki tarafini 6zx^{-\frac{1}{2}}-2 ga bo‘ling.

$$\frac{\left(\frac{6z}{\sqrt{x}}-2\right)y}{\frac{6z}{\sqrt{x}}-2}=\frac{3z}{\frac{6z}{\sqrt{x}}-2}$$

6zx^{-\frac{1}{2}}-2 ga bo'lish 6zx^{-\frac{1}{2}}-2 ga ko'paytirishni bekor qiladi.

$$y=\frac{3z}{\frac{6z}{\sqrt{x}}-2}$$

3z ni 6zx^{-\frac{1}{2}}-2 ga bo'lish.

$$y=\frac{3\sqrt{x}z}{2\left(3z-\sqrt{x}\right)}$$

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{3\sqrt{x}z}{2\left(3z-\sqrt{x}\right)}\text{, }y\neq 0$$

x uchun yechish

$$x=36\times \left(\frac{yz}{2y+3z}\right)^{2}$$

$$\left(y>0\text{ and }y<-\frac{3z}{2}\right)\text{ or }\left(z>0\text{ and }y<-\frac{3z}{2}\right)\text{ or }\left(z>0\text{ and }y>0\right)$$