Question

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

Answer 1

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