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Question 3: If 2^{2x+4} – 17 × 2^{x+1} = –4, then which of the following is true?

- x is a positive value
- x is a negative value
- x can be either a positive value or a negative value
- None of these

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2^{x+4} – 17 * 2^{x+1} = – 4

=> 2^{x+1} = y

2^{2x+2} = y^{2}

2^{2}(2^{2x+2}) – 17 * 2^{x+1} = –4

4y^{2} – 17y + 4 = 0

4y^{2} – 16y – y + 4 = 0

4y (y – 4) – 1 (y – 4) = 0

y = \\frac{1}{4}\\) or 4

2^{x+1} = \\frac{1}{4}\\) or 4

=> x + 1 = 2 or – 2

x = 1 or – 3

The question is **"which of the following is true?"**

Choice C is the correct answer.

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