f 3 P x x 3 find the value of P(1), P(2), P(-1), P(-2).
Answers
Answered by
1
Answer:
Step-by-step explanation:
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
Answered by
0
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= 1/6
p(x)=1/6(x-1)(x-2)(x-3)+x
p(6)=1/6(5)(4)(3)+6=16
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