Question

Solve this equation (Shown in the screenshot below)

Answer 1

x = {-2, 0, 2}

Explanation:

You want the solutions to √((√(x²) -1)²) = 1.

Solution

Squaring both sides gives ...

(√(x²) -1)² = 1² = 1

Taking the square root of both sides gives ...

√(x²) -1 = ±1

Adding 1, we have ...

√(x²) = 1 ± 1 = {0, 2}

We know that √(x²) = |x|, so this reduces to ...

|x| = {0, 2}

x = {±0, ±2}

x = {-2, 0, 2}

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Additional comment

For finding the solutions graphically, we like to plot the equation in the form f(x) = 0. The graphing calculator readily identifies the x-intercepts, which are the solutions.