Question:
Tick (✓) the correct answer:
If (a + b) = 12 and ab = 14, then (a2 + b2) = ?
(a) 172
(b) 116
(c) 165
(d) 126
Solution:
(b) 116
$(a+b)=12$
$\Rightarrow$ Squaring both the sides:
$\Rightarrow(a+b)^{2}=(12)^{2}$
$\Rightarrow\left(a^{2}+b^{2}+2 a b\right)=144$
$\Rightarrow\left(a^{2}+b^{2}\right)=144-2 a b$
$\Rightarrow\left(a^{2}+b^{2}\right)=144-2(14)$
$\Rightarrow\left(a^{2}+b^{2}\right)=144-28$
$\Rightarrow\left(a^{2}+b^{2}\right)=116$
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