If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of $$(a^{2}+b^{2}+c^{2})$$ ?

Given : $$a(a+b+c)=45$$

=> $$a^2+ab+ac=45$$ ------------(i)

Similarly, $$ab+b^2+bc=75$$ ------------(ii)

and $$ac+bc+c^2=105$$ ------------(iii)

Adding equations (i),(ii) and (iii),

=> $$a^2+b^2+c^2+2ab+2bc+2ac=45+75+105$$

=> $$(a+b+c)^2=(15)^2$$

=> $$a+b+c=15$$

Substituting above value in equation (i), => $$a=\frac{45}{15}=3$$

Similarly, $$b=5$$ and $$c=7$$

$$\therefore$$ $$(a^{2}+b^{2}+c^{2})$$

= $$(3)^2+(5)^2+(7)^2$$

= $$9+25+49=83$$

=> Ans - (B)