1/sqrt{x}+1/-x9=1/20 eching

$$\frac{ 1 }{ \sqrt{ x } } + \frac{ 1 }{ -x9 } = \frac{ 1 }{ 20 }$$

x_9 uchun yechish

$$x_{9}=-\frac{20\sqrt{x}\left(\sqrt{x}+20\right)}{x-400}$$

$$x\neq 400\text{ and }x>0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{\sqrt{x}} ni ayirish.

$$\frac{1}{-x_{9}}=\frac{1}{20}-\frac{1}{\sqrt{x}}$$

x_{9} qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 20x_{9} ga, -x_{9},20 ning eng kichik karralisiga ko‘paytiring.

$$-20=20x_{9}\times \frac{1}{20}-20x_{9}x^{-\frac{1}{2}}$$

1 hosil qilish uchun 20 va \frac{1}{20} ni ko'paytirish.

$$-20=x_{9}-20x_{9}x^{-\frac{1}{2}}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x_{9}-20x_{9}x^{-\frac{1}{2}}=-20$$

x_{9}'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1-20x^{-\frac{1}{2}}\right)x_{9}=-20$$

Tenglama standart shaklda.

$$\left(1-\frac{20}{\sqrt{x}}\right)x_{9}=-20$$

Ikki tarafini 1-20x^{-\frac{1}{2}} ga bo‘ling.

$$\frac{\left(1-\frac{20}{\sqrt{x}}\right)x_{9}}{1-\frac{20}{\sqrt{x}}}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

1-20x^{-\frac{1}{2}} ga bo'lish 1-20x^{-\frac{1}{2}} ga ko'paytirishni bekor qiladi.

$$x_{9}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

-20 ni 1-20x^{-\frac{1}{2}} ga bo'lish.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}$$

x_{9} qiymati 0 teng bo‘lmaydi.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}\text{, }x_{9}\neq 0$$

x uchun yechish

$$x=400\times \left(\frac{x_{9}}{x_{9}+20}\right)^{2}$$

$$x_{9}<-20\text{ or }x_{9}>0$$