3y^2-2/5=y eching

$$\frac { 3 y ^ { 2 } - 2 } { 5 } = y$$

y uchun yechish

$$y=-\frac{1}{3}\approx -0,333333333$$

$$y=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{3}{5}y^{2}-\frac{2}{5} natijani olish uchun 3y^{2}-2 ning har bir ifodasini 5 ga bo‘ling.

$$\frac{3}{5}y^{2}-\frac{2}{5}=y$$

Ikkala tarafdan y ni ayirish.

$$\frac{3}{5}y^{2}-\frac{2}{5}-y=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$\frac{3}{5}y^{2}-y-\frac{2}{5}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{3}{5} ni a, -1 ni b va -\frac{2}{5} ni c bilan almashtiring.

$$y=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{3}{5}\left(-\frac{2}{5}\right)}}{2\times \frac{3}{5}}$$

-4 ni \frac{3}{5} marotabaga ko'paytirish.

$$y=\frac{-\left(-1\right)±\sqrt{1-\frac{12}{5}\left(-\frac{2}{5}\right)}}{2\times \frac{3}{5}}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali -\frac{12}{5} ni -\frac{2}{5} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$y=\frac{-\left(-1\right)±\sqrt{1+\frac{24}{25}}}{2\times \frac{3}{5}}$$

1 ni \frac{24}{25} ga qo'shish.

$$y=\frac{-\left(-1\right)±\sqrt{\frac{49}{25}}}{2\times \frac{3}{5}}$$

\frac{49}{25} ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-1\right)±\frac{7}{5}}{2\times \frac{3}{5}}$$

-1 ning teskarisi 1 ga teng.

$$y=\frac{1±\frac{7}{5}}{2\times \frac{3}{5}}$$

2 ni \frac{3}{5} marotabaga ko'paytirish.

$$y=\frac{1±\frac{7}{5}}{\frac{6}{5}}$$

y=\frac{1±\frac{7}{5}}{\frac{6}{5}} tenglamasini yeching, bunda ± musbat. 1 ni \frac{7}{5} ga qo'shish.

$$y=\frac{\frac{12}{5}}{\frac{6}{5}}$$

\frac{12}{5} ni \frac{6}{5} ga bo'lish \frac{12}{5} ga k'paytirish \frac{6}{5} ga qaytarish.

$$y=2$$

y=\frac{1±\frac{7}{5}}{\frac{6}{5}} tenglamasini yeching, bunda ± manfiy. 1 dan \frac{7}{5} ni ayirish.

$$y=-\frac{\frac{2}{5}}{\frac{6}{5}}$$

-\frac{2}{5} ni \frac{6}{5} ga bo'lish -\frac{2}{5} ga k'paytirish \frac{6}{5} ga qaytarish.

$$y=-\frac{1}{3}$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

\frac{3}{5}y^{2}-\frac{2}{5} natijani olish uchun 3y^{2}-2 ning har bir ifodasini 5 ga bo‘ling.

$$\frac{3}{5}y^{2}-\frac{2}{5}=y$$

Ikkala tarafdan y ni ayirish.

$$\frac{3}{5}y^{2}-\frac{2}{5}-y=0$$

\frac{2}{5} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{3}{5}y^{2}-y=\frac{2}{5}$$

Tenglamaning ikki tarafini \frac{3}{5} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{3}{5}y^{2}-y}{\frac{3}{5}}=\frac{\frac{2}{5}}{\frac{3}{5}}$$

\frac{3}{5} ga bo'lish \frac{3}{5} ga ko'paytirishni bekor qiladi.

$$y^{2}+\left(-\frac{1}{\frac{3}{5}}\right)y=\frac{\frac{2}{5}}{\frac{3}{5}}$$

-1 ni \frac{3}{5} ga bo'lish -1 ga k'paytirish \frac{3}{5} ga qaytarish.

$$y^{2}-\frac{5}{3}y=\frac{\frac{2}{5}}{\frac{3}{5}}$$

\frac{2}{5} ni \frac{3}{5} ga bo'lish \frac{2}{5} ga k'paytirish \frac{3}{5} ga qaytarish.

$$y^{2}-\frac{5}{3}y=\frac{2}{3}$$

-\frac{5}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{6} olish uchun. Keyin, -\frac{5}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-\frac{5}{3}y+\left(-\frac{5}{6}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{6} kvadratini chiqarish.

$$y^{2}-\frac{5}{3}y+\frac{25}{36}=\frac{2}{3}+\frac{25}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{3} ni \frac{25}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$y^{2}-\frac{5}{3}y+\frac{25}{36}=\frac{49}{36}$$

y^{2}-\frac{5}{3}y+\frac{25}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-\frac{5}{6}\right)^{2}=\frac{49}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-\frac{5}{6}\right)^{2}}=\sqrt{\frac{49}{36}}$$

Qisqartirish.

$$y-\frac{5}{6}=\frac{7}{6} y-\frac{5}{6}=-\frac{7}{6}$$

\frac{5}{6} ni tenglamaning ikkala tarafiga qo'shish.

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