p-x-xp-x-x-2-1-faind-p-2-

Question Number 164135 by mathlove last updated on 14/Jan/22

p (x) + x p (- x) = x^{2} + 1

f a i n d p (2) = ?

Answered by mr W last updated on 14/Jan/22

p (x) + x p (- x) = x^{2} + 1 \dots (i)

p (- x) - x p (x) = x^{2} + 1

x p (- x) - x^{2} p (x) = (x^{2} + 1) x \dots (i i)

(i) - (i i) :

(1 + x^{2}) p (x) = (x^{2} + 1) (1 - x)

\Rightarrow p (x) = 1 - x

\Rightarrow p (2) = 1 - 2 = - 1

Commented by mathlove last updated on 14/Jan/22

t h a n k s t h e a r m r W

Commented by mathlove last updated on 14/Jan/22

Commented by mr W last updated on 14/Jan/22

l o o k a b o v e a g a i n!

Commented by mathlove last updated on 14/Jan/22

t h a n k I k n o w