y=2y+3/3y-2 eching

$$y= \frac{ 2y+3 }{ 3y-2 }$$

y uchun yechish

$$y = \frac{\sqrt{13} + 2}{3} \approx 1,868517092$$

$$y=\frac{2-\sqrt{13}}{3}\approx -0,535183758$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{2y+3}{3y-2} ni ayirish.

$$y-\frac{2y+3}{3y-2}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y ni \frac{3y-2}{3y-2} marotabaga ko'paytirish.

$$\frac{y\left(3y-2\right)}{3y-2}-\frac{2y+3}{3y-2}=0$$

\frac{y\left(3y-2\right)}{3y-2} va \frac{2y+3}{3y-2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{y\left(3y-2\right)-\left(2y+3\right)}{3y-2}=0$$

y\left(3y-2\right)-\left(2y+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3y^{2}-2y-2y-3}{3y-2}=0$$

3y^{2}-2y-2y-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3y^{2}-4y-3}{3y-2}=0$$

y qiymati \frac{2}{3} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3y-2 ga ko'paytirish.

$$3y^{2}-4y-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -4 ni b va -3 ni c bilan almashtiring.

$$y=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 3\left(-3\right)}}{2\times 3}$$

-4 kvadratini chiqarish.

$$y=\frac{-\left(-4\right)±\sqrt{16-4\times 3\left(-3\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$y=\frac{-\left(-4\right)±\sqrt{16-12\left(-3\right)}}{2\times 3}$$

-12 ni -3 marotabaga ko'paytirish.

$$y=\frac{-\left(-4\right)±\sqrt{16+36}}{2\times 3}$$

16 ni 36 ga qo'shish.

$$y=\frac{-\left(-4\right)±\sqrt{52}}{2\times 3}$$

52 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-4\right)±2\sqrt{13}}{2\times 3}$$

-4 ning teskarisi 4 ga teng.

$$y=\frac{4±2\sqrt{13}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$y=\frac{4±2\sqrt{13}}{6}$$

y=\frac{4±2\sqrt{13}}{6} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{13} ga qo'shish.

$$y=\frac{2\sqrt{13}+4}{6}$$

4+2\sqrt{13} ni 6 ga bo'lish.

$$y=\frac{\sqrt{13}+2}{3}$$

y=\frac{4±2\sqrt{13}}{6} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{13} ni ayirish.

$$y=\frac{4-2\sqrt{13}}{6}$$

4-2\sqrt{13} ni 6 ga bo'lish.

$$y=\frac{2-\sqrt{13}}{3}$$

Tenglama yechildi.

$$y=\frac{\sqrt{13}+2}{3} y=\frac{2-\sqrt{13}}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{2y+3}{3y-2} ni ayirish.

$$y-\frac{2y+3}{3y-2}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y ni \frac{3y-2}{3y-2} marotabaga ko'paytirish.

$$\frac{y\left(3y-2\right)}{3y-2}-\frac{2y+3}{3y-2}=0$$

\frac{y\left(3y-2\right)}{3y-2} va \frac{2y+3}{3y-2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{y\left(3y-2\right)-\left(2y+3\right)}{3y-2}=0$$

y\left(3y-2\right)-\left(2y+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3y^{2}-2y-2y-3}{3y-2}=0$$

3y^{2}-2y-2y-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3y^{2}-4y-3}{3y-2}=0$$

y qiymati \frac{2}{3} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3y-2 ga ko'paytirish.

$$3y^{2}-4y-3=0$$

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

$$3y^{2}-4y=3$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3y^{2}-4y}{3}=\frac{3}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$y^{2}-\frac{4}{3}y=\frac{3}{3}$$

3 ni 3 ga bo'lish.

$$y^{2}-\frac{4}{3}y=1$$

-\frac{4}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{2}{3} olish uchun. Keyin, -\frac{2}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-\frac{4}{3}y+\left(-\frac{2}{3}\right)^{2}=1+\left(-\frac{2}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{2}{3} kvadratini chiqarish.

$$y^{2}-\frac{4}{3}y+\frac{4}{9}=1+\frac{4}{9}$$

1 ni \frac{4}{9} ga qo'shish.

$$y^{2}-\frac{4}{3}y+\frac{4}{9}=\frac{13}{9}$$

y^{2}-\frac{4}{3}y+\frac{4}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-\frac{2}{3}\right)^{2}=\frac{13}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-\frac{2}{3}\right)^{2}}=\sqrt{\frac{13}{9}}$$

Qisqartirish.

$$y-\frac{2}{3}=\frac{\sqrt{13}}{3} y-\frac{2}{3}=-\frac{\sqrt{13}}{3}$$

\frac{2}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$y=\frac{\sqrt{13}+2}{3} y=\frac{2-\sqrt{13}}{3}$$