If $a+b = 5$ and $ab =2$, find the value of $a^2+b^2$.

Given:

\( a+b=5 \) and \( a b=2 \)

To do:

We have to find the value of \( (a+b)^{2} \).

Solution:

We know that,

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

Therefore,

$a^2+b^2=(a+b)^2-2(ab)$

$=(5)^2-2(2)$

 $=25-4$

$=21$