Question

Sendo a + b = 4 e a - b = 2, determine o valor de a² - b².

Answer 1

a=2+b
2+b+b=4
2b=2
b=1
a=2+1
a=3
3²-1²
9-1=8
a²-b²=8

Answer 2

$\begin{cases}a+b=4\\ a-b=2\end{cases}\\\\\\a+b=4\to~~a=-b+4\\\\\\ a-b=2\to~~ -b+4-b=2\to~~ -b-b=2-3\to\\\\-2b=-2\to~(-1)\to~~ 2b=2\to~~b= \dfrac{2}{2} \to~~ \boxed{b=1}\\\\\\a=-b+4\to~~a=-1+4\to~~\boxed{a=3}$




$a^2-b^2\to~~3^2-1^2\to~~9-1\to~~\large\boxed{8}$