2.5-bo'lim : Kvadrat tenglamalar - I qism
4. Quyidagi kvadrat tenglamani ko'paytuvchilarga ajratish yordamida yeching.
\[19x = 7 - 6{x^2}\]Yechim
Biz qilishimiz kerak bo'lgan birinchi narsa - tenglamaning bir tomonida hamma narsani olish va keyin kvadratik faktor.
\[\begin{align*}6{x^2} + 19x - 7 & = 0\\ \left( {3x - 1} \right)\left( {2x + 7} \right) & = 0\end{align*}\]2-qadam
Endi biz qilishimiz kerak bo'lgan narsa, olish uchun nol omil xususiyatidan foydalanishdir,
\[\begin{array}{*{20}{c}}{3x - 1 = 0}\\{\displaystyle x = \frac{1}{3}}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{2x + 7 = 0}\\{\displaystyle x = - \frac{7}{2}}\end{array}\]Shuning uchun ikkita yechim: \(\require{bbox} \bbox[2pt,border:1px solid black]{{x = \frac{1}{3}\,\,{\mbox{and }}x = - \frac{7}{2}}}\)
Agar xohlasangiz, ularni tenglamaga qayta ulash orqali ular haqiqatan ham yechim ekanligini tekshirishni sizga qoldiramiz.