2.6-bo'lim : Kvadrat tenglamalar - II qism
9. Quyidagi kvadrat tenglamani yechish uchun kvadrat formuladan foydalaning.
\[{x^2} - 6x + 4 = 0\]Yechim
Haqiqatan ham bu muammo uchun juda ko'p narsa yo'q. Birinchidan, kvadratik formula uchun qiymatlarni aniqlashimiz kerak.
\[a = 1\hspace{0.25in}b = - 6\hspace{0.25in}c = 4\]2-qadam
Bularni kvadratik formulaga kiritish,
\[x = \frac{{ - \left( { - 6} \right) \pm \sqrt {{{\left( { - 6} \right)}^2} - 4\left( 1 \right)\left( 4 \right)} }}{{2\left( 1 \right)}} = \frac{{6 \pm \sqrt {20} }}{2} = \frac{{6 \pm 2\sqrt 5 }}{2} = 3 \pm \sqrt 5 \]Bu tenglamaning ikkita yechimi quyidagicha bo'ladi: \[\require{bbox} \bbox[2pt,border:1px solid black]{{x = 3 - \sqrt 5 \,\,{\mbox{and }}x = 3 + \sqrt 5 }}\].