Question

# The sum of all real values of x satisfying the equation (x2−5x+5)(x2+4x−60)=1 is 653−4

Solution

## The correct option is C 3CASE 1: x2+4x−60 can be any real number and x2−5x+5=1 i.e. x2−5x+4=0 ⇒x=1,4  CASE 2: x2+4x−60=0 and x2−5x+5 can be any real number except 0 as 00 is undefined. i.e. (x+10)(x−6)=0 ⇒x=6,−10  and x2−5x+5≠0 ⇒x≠5±√52 CASE 3: (−1)even=1 i.e. x2−5x+5=−1 and x2+4x−60 is an even number   ⇒x2−5x+6=0 ⇒(x−2)(x−3)=0 ⇒x=2,3 At x=2, the value of x2+4x−60 is (2)2+4(2)−60=−48 Which is even At x=3, the value of x2+4x−60 is (3)2+4(3)−60=−39 Which is odd   ∴x=3 is rejected  Sum of all the real values of x=1+4+6−10+2=3

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