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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2016 · 3 April · Mathematics · Quadratic Equation

The sum of all real values of x satisfying the equation ( x ^ 2 -...

The sum of all real values of xx satisfying the equation (x2−5x+5)x2+4x−60=1{\left({x}^{2} - 5x + 5\right)}^{{x}^{2} + 4x - 60} = 1 is

Options

  1. A66
  2. B55
  3. C33
  4. D−4- 4

Correct answer

C. 33

Step-by-step solution

The given equation will be true in 33 cases.

Case 1: when x2−5x+5=1{x}^{2} - 5x + 5 = 1

⇒x2−5x+4=0⇒ {x}^{2} - 5x + 4 = 0

⇒x=1,4⇒ x = 1, 4

Case 2: when x2+4x−60=0{x}^{2} + 4x - 60 = 0

⇒x=6,−10⇒ x = 6, - 10

Case 3: when x2−5x+5=−1{x}^{2} - 5x + 5 = - 1 and x2+4x−60∈{x}^{2} + 4x - 60 \in even integers

Now, x2−5x+5=−1{x}^{2} - 5x + 5 = - 1

⇒x=2,3⇒ x = 2, 3

Only x=2x = 2 satisfies the given condition,

Hence, sum of all real values of xx is 1+4+6−10+21 + 4 + 6 - 10 + 2=3= 3
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