Question

If $a-b=4$ and $a+b=6$; find $a^2+b^2$ and $ab$.

Answer 1

$a+b=6$

$(a+b{)}^2=36$ __(1)

$a-b=4$

$(a-b{)}^2=16$ __(2)

adding (1) & (2) we get

$(a+b{)}^2+(a-b{)}^2=a^2+b^2+2ab+a^2+b^2-2ab=52$

$2(a^2+b^2)=52$

$a^2+b^2=26$

$a+b=6$ __(1)

$a-b=4$ __(2)

____________

$2a=10$

$a=5$

Substitute $a=5$ in any of equations (1) & (2)

$5+b=6$

$b=1$

$ab=\left(5\right)\left(1\right)$

$=5$