t² + 7z + 9z² = t² + 2 · 3z · 7/6 = 49/36 + 7z + 9z² = (7/6)² + 7z + 9z² =
= (7/6 + 3z)²
ответ: t = 7/6
![\boxed {(a+b)^2=a^2+2ab+b^2}\\\\\\t^2+7z+9z^2=\underbrace{t^2}_{a^2}+\underbrace {2\cdot \frac{7}{2\cdot 3}\cdot 3z}_{2ab}+\underbrace {(3z)^2}_{b^2}=\\\\=\Big [\; 2ab=2\cdot \frac{7}{6}\cdot 3z\; \; \to \; \; a=\frac{7}{6}\; \Big ]=(\frac{7}{6})^2+2\cdot \frac{7}{6}\cdot 3z+(3z)^2=\\\\=\frac{49}{36}+7z+9z^2\\\\t=\frac{7}{6}](/tpl/images/0032/7414/a2af3.png)