Discussion Forum

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 :

Answer:

Explanation:

$a^{2}+b^{2}=45$----(1)
$b^{2}+c^{2}=40$----(2)
Subtracting we get, $a^{2}-c^{2}=5$
$\Rightarrow (a+c)(a-c)=5$
$\therefore$ $(a+c)=5$----(3) and $(a-c)=1$----(4)
Sovling, we get : 2a = 6 $\therefore$ a =3
Put value of a in equ.(3), we get c = 2
Put value of a in equ.(1), we get $b^{2}=36$
$\therefore$ b = 6.
So values of a, b, c are (3, 6, 2) respectively