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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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Explanatory Answer

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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