Pregunta
Use the square root property to solve the equation. \[ (x-17)^{2}=17 \]
Ask by Young Luna. in the United States
Mar 01,2025
Solución de inteligencia artificial de Upstudy
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The solutions are \( x = 17 + \sqrt{17} \) and \( x = 17 - \sqrt{17} \).
Solución
Given the equation (x - 17)² = 17, we use the square root property, which tells us that if a² = b, then a = √b or a = -√b (assuming b is non-negative).
Step 1. Write the equation:
(x - 17)² = 17
Step 2. Apply the square root property:
x - 17 = √17 or x - 17 = -√17
Step 3. Solve for x by adding 17 to both sides:
x = 17 + √17 or x = 17 - √17
So, the solutions are:
x = 17 + √17 and x = 17 - √17.
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Simplifique esta solución Mind Expander
To solve the equation \((x-17)^{2}=17\) using the square root property, we first take the square root of both sides. This gives us two possible equations: \[ x - 17 = \sqrt{17} \] or \[ x - 17 = -\sqrt{17} \] Now, we solve for \(x\) in each case. 1. For \(x - 17 = \sqrt{17}\): \[ x = 17 + \sqrt{17} \] 2. For \(x - 17 = -\sqrt{17}\): \[ x = 17 - \sqrt{17} \] Thus, the solutions to the equation are: \[ x = 17 + \sqrt{17} \quad \text{and} \quad x = 17 - \sqrt{17} \]
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