If $ a+b=5 $ and $ a b=2 $, find the value of
(a) $ (a+b)^{2} $
(b) $ a^{2}+b^{2} $
(c) $ (a-b)^{2} $

Given:

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

To do:

We have to find the value of

(a) \( (a+b)^{2} \)

(b) \( a^{2}+b^{2} \)

(c) \( (a-b)^{2} \)

Solution:

We know that,

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

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

Therefore,

(a) $(a+b)^2=(5)^2$

$=25$

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

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

 $=25-4$

$=21$

 (c) $(a-b)^2=a^2+b^2-2ab$

$=21-2(2)$

$=21-4$

$=17$