Let a, b, c [ R].

Question

Let $a$, b, c $$ \in R$$. If $$f(x) = ax2 + bx + c is such that

$a$ + b + c = 3 and \[f(x + y) = \[f(x) + \[f(y) + xy, \[\forall x,y \in R,$$

then $$\sum\limits_{n = 1}^{10} {f(n)} $$ is equal to

Accepted Answer

f(x) = ax2 + bx + c

f(1) = a + b + c = 3 $$ \Rightarrow $$ f (1) = 3

Now f(x + y) = f(x) + f(y) + xy ...(1)

Put x = y = 1 in eqn (1)

f(2) = f(1) + f(1) + 1

= 2f(1) + 1

$$ \Rightarrow $$ f(2) = 7

Similarly f(3) = 12

f(4) = 18

$$\sum\limits_{n = 1}^{10} {f(n)} $$ = 3 + 7 + 12 + 18 + 25 + 33 + 42 + 52 + 63 + 75 = 330

Solutions · 1