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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)$
$=21-4$
$=17$
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