Question:
Tick (✓) the correct answer:
If (a − b) = 7 and ab = 9, then (a2 + b2) = ?
(a) 67
(b) 31
(c) 40
(d) 58
Solution:
(a) 67
$(a-b)=7$
$\Rightarrow$ Squaring both the sides :
$\Rightarrow(a-b)^{2}=(7)^{2}$
$\Rightarrow\left(a^{2}+b^{2}-2 a b\right)=49$
$\Rightarrow\left(a^{2}+b^{2}\right)=49+2 a b$
$\Rightarrow\left(a^{2}+b^{2}\right)=49+2(9)$
$\Rightarrow\left(a^{2}+b^{2}\right)=49+18$
$\Rightarrow\left(a^{2}+b^{2}\right)=67$
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