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a^(2)+1=0 How many distinct real solutions does the given equation have? ◻

a2+1=0a^{2}+1=0\newlineHow many distinct real solutions does the given equation have?\newline□\square

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Full solution

Q. a2+1=0a^{2}+1=0\newlineHow many distinct real solutions does the given equation have?\newline□\square
  1. Isolate a2a^2: First, let's try to isolate a2a^2 by subtracting 11 from both sides of the equation.\newlinea2+1−1=0−1a^2 + 1 - 1 = 0 - 1\newlinea2=−1a^2 = -1
  2. Real Number Squares: Now, we know that a2a^2 is the square of a real number, and the square of a real number can't be negative.\newlineSo, there's no real number that when squared gives −1-1.\newlineThis means there are no real solutions to the equation.

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