3/x=1/x^2quad4/2x eching

$$\frac { 3 } { x } = \frac { 1 } { x ^ { 2 } } \quad \frac { 4 } { 2 x }$$

x uchun yechish

$$x=\frac{\sqrt{6}}{3}\approx 0,816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0,816496581$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x^{2} ga, x,x^{2},2x ning eng kichik karralisiga ko‘paytiring.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$6x=2\times 1\times \frac{4}{2x}$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$6x=2\times \frac{4}{2x}$$

2\times \frac{4}{2x} ni yagona kasrga aylantiring.

$$6x=\frac{2\times 4}{2x}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$6x=\frac{4}{x}$$

Ikkala tarafdan \frac{4}{x} ni ayirish.

$$6x-\frac{4}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 6x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

\frac{6xx}{x} va \frac{4}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{6xx-4}{x}=0$$

6xx-4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{6x^{2}-4}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$6x^{2}-4=0$$

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

$$6x^{2}=4$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=\frac{4}{6}$$

\frac{4}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{2}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x^{2} ga, x,x^{2},2x ning eng kichik karralisiga ko‘paytiring.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$6x=2\times 1\times \frac{4}{2x}$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$6x=2\times \frac{4}{2x}$$

2\times \frac{4}{2x} ni yagona kasrga aylantiring.

$$6x=\frac{2\times 4}{2x}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$6x=\frac{4}{x}$$

Ikkala tarafdan \frac{4}{x} ni ayirish.

$$6x-\frac{4}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 6x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

\frac{6xx}{x} va \frac{4}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{6xx-4}{x}=0$$

6xx-4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{6x^{2}-4}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$6x^{2}-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 0 ni b va -4 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-4\right)}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\left(-4\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\left(-4\right)}}{2\times 6}$$

-24 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{96}}{2\times 6}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{6}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{6}}{12}$$

x=\frac{0±4\sqrt{6}}{12} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{6}}{3}$$

x=\frac{0±4\sqrt{6}}{12} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{6}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$