Question

If p (x)= 2 + X/2 + X^2 - X^2/3 , then find the value of p(–1). (calculations pls)

Answer 1

Answer:

If p^2x (p^2 +1) = p (p^3x+p^x), then is the value of x equal to (A) +1 or -1 (B) + p (C) 0 (D) 1/p?

Given that

p2x[p2+1]=p[p3x+px]

Now,let m=px

Then the given equation changes to

m2[p2+1]=p[m3+m]

⇒m[p(m2+1)−m(p2+1)]=0

⇒px=0….(1)

If p≠0 then (1) has no solution.

And p(m2+1)−m(p2+1)=0

⇒pm2−(p2+1)m+p=0

⇒m=p2+1±(p2+1)2–4p2√2p

⇒m=p2+1±(p2–1)2p

Now,we take positive sign……then we get

m=2p22p

⇒m=p

⇒px=p

⇒x=1

Again,take negative sign,then we get…

m=p2+1−p2+12p

⇒m=1p

⇒px=p−1

⇒x=−1

Hence the required value of x is

−1,+1 .(Ans)