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

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