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x2−1=0x^2-1=0, solve for xx.

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Full solution

Q. x2−1=0x^2-1=0, solve for xx.
  1. Recognize Equation as Difference of Squares: Recognize the equation x2−1=0x^2 - 1 = 0 as a difference of squares.\newlineThe equation can be factored using the difference of squares formula, which is a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b).\newlineHere, a=xa = x and b=1b = 1, so we can rewrite the equation as (x+1)(x−1)=0(x + 1)(x - 1) = 0.
  2. Factor Using Formula: Apply the zero product property.\newlineIf the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for xx.\newlinex+1=0x + 1 = 0 or x−1=0x - 1 = 0
  3. Apply Zero Product Property: Solve each equation for xx.\newlineFirst equation: x+1=0x + 1 = 0\newlineSubtract 11 from both sides to isolate xx.\newlinex=−1x = -1\newlineSecond equation: x−1=0x - 1 = 0\newlineAdd 11 to both sides to isolate xx.\newlinex=1x = 1

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