Final answer:
To solve the equation 3√x = |x-2|-1, follow these steps: square both sides, simplify the equation, rewrite as a quadratic equation, bring all terms to one side, and use the quadratic formula to find solutions for x.
Step-by-step explanation:
To solve the equation 3√x = |x-2|-1, we need to isolate x. Here are the steps:
Square both sides of the equation to eliminate the square root: (3√x)2 = (|x-2|-1)2
Simplify the equation by expanding the squared terms: 9x = (x-2)2 - 2|x-2| + 1
Simplify further and rewrite the equation as a quadratic equation: 9x = x2 - 4x + 4 - 2x + 4 - 2 + 1
Bring all terms to one side to get a quadratic equation: x2 - 15x + 15 = 0
Use the quadratic formula to find the solutions for x: x = (-b ± √(b^2 - 4ac))/(2a), where
a = 1,
b = -15, and
c = 15
The two possible solutions for x are
x = 0.0216 or
x = -0.0224.