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Question

If the LCM of f(x)=(x+1)5(x+2)a and g(x)=(x+1)b(x+2)a is (x+1)a(x+2)b, then the value of (a+b) is

A
5
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B
15
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C
10
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D
12
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Solution

The correct option is C 10
Given that f(x)=(x+1)5(x+2)a and g(x)=(x+1)b(x+2)a
Given that LCM of f(x),g(x) is (x+1)a(x+2)b
Observe (x+1) powers in f(x),g(x) , we can see that LCM of 5,b must be a
Observe (x+2) powers in f(x),g(x) , We can see that LCM of a,a must be b
LCM of a,a is a=b
Since a=b , LCM of 5,b is equivalent to LCM of 5,a , Given that it is equal to a
Therefore a must be equal to 5
So the value of a+b=5+5=10
Therefore the correct option is C

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