Question

ПОМОГИТЕ ПРОШУ!!!!!
Заміни t одночленном так, щоб вийшов квадрат двочлена
t+7x+36x²

Answer 1

$frac{49}{144}+7x+36x^{2}=(frac{7}{12}+6x)^{2}$

Answer 2

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