Question

ПОМОГИТЕ ПРОШУ!!
Заміни k одночленном так, щоб вийшов квадрат двочлена
k+7z+36z²

Answer 1

$k+7z+36z^2=k+\underbrace {2\cdot \frac{1}{2}\cdot 7z}_{2ab}+\underbrace {(6z)^2}_{b^2}=k+\underbrace {2\cdot \frac{7z}{2}\cdot \frac{6z}{6z}}_{2ab}+\underbrace {(6z)^2}_{b^2}=\\\\\\=k+\underbrace {2\cdot \frac{7z}{2\cdot 6z}}_{2\cdot a}\cdot \underbrace {6z}_{b}+\underbrace {(6z)^2}_{b^2}=\underbrace {\Big (\frac{7}{12}\Big )^2}_{a^2}+\underbrace {2\cdot \frac{7}{12}\cdot 6z}_{2ab}+\underbrace {(6z)^2}_{b^2}=\\\\\\=\frac{49}{144} +2\cdot \frac{7}{12}\cdot 6z+(6z)^2=\Big (\frac{7}{12}+6z\Big )^2\; ,\\\\k=\frac{49}{144}$