If $a, b, c$ are integers; $a^{2}+b^{2}=45$ and $b^{2}+c^{2}=40$, then the values of $a, b$ and $c$ respectively are
(a)2, 6, 3
(b)3, 2, 6
(c)5, 4, 3
(d)None of these
Answer
Answer (as printed): D
Explanation
$a^{2}+b^{2}=45$ $$\text { and } b^{2}+c^{2}=40$$ Subtracting, we get: $a^{2}-c^{2}=5 \Rightarrow(a+c)(a-c)=5$. $$\therefore \quad(a+c)=5 \text { and }(a-c)=1 .$$ Solving, we get: $a=3, c=2$. Putting $c=2$ in (ii), we get: $b=6$.
Explanation as extracted from the printed page; notation may be imperfect.