Question

If the values of $a+b$ and $a-b$ are $7$ and $4$ respectively, find the values of $a^2+b^2$ and $ab$

Answer 1

(i) $a^2+b^2=\frac{1}{2}\left[\right(a+b{)}^2+(a-b{)}^2]$
$=\frac{1}{2}[7^2+4^2]$ ------[Substituting the values of $a+b=7,a-b=4]$
$=\frac{1}{2}(49+16)$
$=\frac{1}{2}\left(65\right)$

$=\frac{65}{2}$
$a^2+b^2=\frac{65}{2}$
(ii) $ab=\frac{1}{4}\left[\right(a+b{)}^2-(a-b{)}^2]$
$=\frac{1}{4}(7^2-4^2)$ -------- [Substituting the values of $a+b=7,a-b=4]$
$=\frac{1}{4}(49-16)$
$=\frac{1}{4}\left(33\right)$
$ab=\frac{33}{4}$