# CAT 2020 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 6

Solving questions from Linear and Quadratic equations is an integral part of your CAT preparation. In CAT Exam, one can generally expect to get 1~2 questions from Linear Equations and Quadratic Equations. In this question, we have to find the number of real-valued solutions. Would something conventional work or, do we have to take some non-formulaic approach? Find it out yourself. Time to have a go at this question, and then check out the video solution to find out how Rajesh solves this question!

Question 6 : The number of real-valued solutions of the equation 2x + 2-x = 2 - (x - 2)2 is

1. infinite
2. 0
3. 1
4. 2

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2x + 2-x is of the form y + $$frac{1}{y}$ Minimum value the expression can take is ≥ 2 So 2x + 2-x ≥ 2 Now, 2 –$x – 2)2 ----> (x – 2)2 is ≥ 0
So 2 – (x – 2)2 ≤ 2 (From 2 we are subtracting a non-negative number)
Maximum value the expression can have is 2
The only possibility is both sides are = 2
If value = 2
Then x = 0
20 + 20 = 2 – (0 – 2)2
2 ≠ – 2
There is no case where LHS = RHS = 2
Hence 0 real-valued solutions

The question is "The number of real-valued solutions of the equation 2x + 2-x = 2 - (x - 2)2 is"

##### Hence, the answer is, "0"

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