The sum of all real values of x satisfying the equation x 2 - 5 x + 5 x 2 + 4 x - 60 = 1 is

The sum of all real values of x satisfying the equation x2-5x+5x2+4x-60=1 is
  1. 6
  2. 5
  3. 3
  4. -4

Solution

The given equation will be true in 3 cases.

Case 1: when x2-5x+5=1  

⇒x2-5x+4=0

⇒x=1, 4

Case 2: when x2+4x-60=0

⇒x=6, -10

Case 3: when x2-5x+5=-1 and x2+4x-60∈ even integers

Now, x2-5x+5=-1    

⇒x=2, 3

Only x=2 satisfies the given condition,

Hence, sum of all real values of x is 1+4+6-10+2=3 

Asked in: JEE Main 2016 (03 Apr)

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