Find the value of
p1
3
×
−
1
8
=
p
×
1
3
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ANSWER
Given P(1)=1,P(2)=2,P(3)=3,P(4)=5
Let f(x)=(P(x)−x)
f(1)=P(1)−1=1−1=0
f(2)=P(2)−2=2−2=0
f(3)=P(3)−3=3−3=0
∴f(x)=0,x=1,2,3
⇒f(x)=a(x−1)(x−2)(x−3)
P(x)=a(x−1)(x−2)(x−3)+x
Put x=4
5=a(3)(2)(1)+4
⇒a=
6
1
∴P(x)=
6
1
(x−1)(x−2)(x−3)+x
∴P(6)=
6
1
(5)(4)(3)+6=16
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