Question

Let c, k∈ R. If f(x) = (c + 1)x² + (1 – c²)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ......+f (20))| is equal to _____.

Answer 1

Correct Answer: 3395

The correct answer is: 3395

f(x) is polynomial

Put y = 1/x in given functional equation we get

\(f(x+\frac{1}{x})=f(x)+f(\frac{1}{x})-1\)

⇒ 2(c + 1) = 2K – 1 …(1)

and put x = y = 0 we get

\(f(0)=2+f(0)-0⇒f(0)=0⇒k=0\)

∴ k = 0 and 2c = –3 ⇒c = \(–\frac{3}{2}\)

by simplifying we will get

\(=|-\frac{6790}{2}|=3395\)