Question

Qual a terça parte do valor de m² + n², sabendo que (m - n)² = 15 e m.n = 9?

Answer 1

$\displaystyle \text{ter{\c c}a parte de } \text m^2+\text n^2, \text {tendo} : \\\\ (\text m-\text n)^2=15 \ \ ; \ \ \text{m.n}=9\ \ ; \frac{\text m^2+\text n^2}{3}= \ ? \\\\ \underline{\text{desenvolvendo}}: \\\\ (\text m-\text n)^2=\text m^2+\text n^2-2.\text{m.n} \\\\ 15 = \text m^2+\text n^2-2.9 \\\\ \text m^2+\text n^2 = 15 +18 \\\\ \text m^2+\text n^2 = 33$

Dividindo por 3, temos :

$\displaystyle \frac{\text m^2+\text n^2}{3}=\frac{33}{3} \\\\\\ \huge\boxed{\ \frac{\text m^2+\text n^2}{3}=11\ } \checkmark$