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Question 17 : The number of integers that satisfy the equality (x² - 5x + 7)^{x + 1} = 1 is

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Video Explanation

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Explanatory Answer

We can have three possibilities for the equality of form xⁿ = 1
First n = 0, then x = 1 and then x = -1 and n = even (-1)^Even
Using first x = -1, and substituting in given equation
(-1)² -5(-1) + 7 = 8 (Acceptable)
Using second condition, x²
Solving x = 2 or x = 3 (Both are acceptable)
Last condition x2 -5x + 7 = -1
x² -5x + 8 = 0
No integer values,
So 3 values satisfy the equality

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The question is "The number of integers that satisfy the equality (x² - 5x + 7)^{x + 1} = 1 is"

Hence, the answer is, "3"

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