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Question

The sum of all real values of x satisfying the equation (x25x+5)(x2+4x60)=1 is 
  1. 6
  2. 5
  3. 3
  4. 4


Solution

The correct option is C 3
CASE 1:
x2+4x60 can be any real number and x25x+5=1
i.e. x25x+4=0
x=1,4 

CASE 2:
x2+4x60=0 and x25x+5 can be any real number except 0 as 00 is undefined.
i.e. (x+10)(x6)=0
x=6,10 
and x25x+50
x5±52

CASE 3:
(1)even=1
i.e. x25x+5=1 and x2+4x60 is an even number  

x25x+6=0
(x2)(x3)=0
x=2,3

At x=2, the value of x2+4x60 is
(2)2+4(2)60=48
Which is even
At x=3, the value of x2+4x60 is
(3)2+4(3)60=39
Which is odd  
x=3 is rejected 

Sum of all the real values of x=1+4+610+2=3  
 

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