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If a^(3)-3a^(2)+5a-17=0 and b^(3)-3b^(2)...

If `a^(3)-3a^(2)+5a-17=0` and `b^(3)-3b^(2)+5b+11=0` are such that `a+b` is a real number, then the value of `a+b` is

A

`-1`

B

`1`

C

`2`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Let `a+b=lambdaimpliesb=lambda-a`
So `(lambda-a)^(3)-3(lambda-a)^(2)+5(lambda-a)+11=0`
`lambda^(3)-a^(3)-3lambda^(2)a+3lambdaa^(2)-3lambda^(2)+6lambda a-3a^(2)+5lambda-5a+11=0` ,brgt `implies a^(3)+(3-3lambda)a^(2)+(3lambda^(2)-6lambda+5)a-(lambda^(3)-3lambda^(2)+5lambda+11)=0`
Comparing it with the equation `a^(3)-3a^(2)+5a-17=0`, we get `lambda=2`
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