Question

Заміни m одночленном так, щоб вийшов квадрат двочлена
64y²−5y+m

Answer 1

$64y^2-5y+m=\underbrace {(8y)^2}_{a^2}-\underbrace {2\cdot \frac{1}{2}\cdot 5y\cdot \frac{8y}{8y}}_{-2ab}+\underbrace {m}_{b^2}=\Big [\; a=8y\; \Big ]=\\\\\\=(8y)^2-\underbrace {2\cdot 8y\cdot \frac{5y}{2\cdot 8y}}_{2\cdot a\cdot b}+m=(8y)^2-\underbrace {2\cdot 8y\cdot \frac{5}{16}}_{2\cdot a\cdot b}+\Big (\frac{5}{16}\Big )^2=\Big [\; b=\frac{5}{16}\; \Big ]=\\\\\\=(8y)^2-2\cdot 8y\cdot \frac{5}{16}+\frac{25}{256}=(8y-\frac{5}{16})^2\; ,\\\\m=\frac{25}{256}$