2.5-bo'lim : Kvadrat tenglamalar - I qism
7. Quyidagi kvadrat tenglamani ko'paytuvchilarga ajratish yordamida yeching.
\[12{x^2} = 25x\]Yechim
Biz qilishimiz kerak bo'lgan birinchi narsa - tenglamaning bir tomonida hamma narsani olish va keyin kvadratik faktor.
\[\begin{align*}12{x^2} - 25x & = 0\\ x\left( {12x - 25} \right) & = 0\end{align*}\]\(x\) ni tenglamaning har ikki tomonidan bekor qilmasligingizga ishonch hosil qiling!
2-qadam
Endi biz qilishimiz kerak bo'lgan narsa, olish uchun nol omil xususiyatidan foydalanishdir,
\[\begin{array}{*{20}{c}}{x = 0}\\{}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{12x - 25 = 0}\\{\displaystyle x = \frac{{25}}{{12}}}\end{array}\]Shuning uchun ikkita yechim: \(\require{bbox} \bbox[2pt,border:1px solid black]{{x = 0\,\,{\mbox{and }}x = \frac{{25}}{{12}}}}\)
E'tibor bering, agar biz birinchi bosqichda tenglamaning har ikki tomonidan \(x\) ni bekor qilganimizda \(x = 0\) yechimini o'tkazib yuborgan bo'lardik!