2.6-bo'lim : Kvadrat tenglamalar - II qism
11. Quyidagi kvadrat tenglamani yechish uchun kvadrat formuladan foydalaning.
\[8{u^2} + 5u + 70 = 5 - 7u\]Yechim
Birinchidan, kvadrat tenglamani standart shaklda olishimiz kerak. Bu,
\[8{u^2} + 12u + 65 = 0\]2-qadam
Endi kvadrat formula uchun qiymatlarni aniqlashimiz kerak.
\[a = 8\hspace{0.25in}b = 12\hspace{0.25in}c = 65\]3-qadam
Bularni kvadratik formulaga kiritish,
\[u = \frac{{ - 12 \pm \sqrt {{{\left( {12} \right)}^2} - 4\left( 8 \right)\left( {65} \right)} }}{{2\left( 8 \right)}} = \frac{{ - 12 \pm \sqrt { - 1936} }}{{16}} = \frac{{ - 12 \pm 44i}}{{16}} = \frac{{ - 3 \pm 11i}}{4}\]Bu tenglamaning ikkita yechimi quyidagicha bo'ladi: \[\require{bbox} \bbox[2pt,border:1px solid black]{{u = \frac{{ - 3}}{4} - \frac{{11}}{4}i\,\,{\mbox{and }}u = \frac{{ - 3}}{4} + \frac{{11}}{4}i}}\].