Math Problem Statement
\sqrt{x}-\sqrt{x-2}=1
Solution
To solve the equation , follow these steps:
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Isolate one of the square root terms:
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Square both sides to eliminate the square root on the left:
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Expand the right-hand side:
Simplify the equation:
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Subtract from both sides:
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Isolate the remaining square root term:
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Divide both sides by 2:
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Square both sides again to eliminate the square root:
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Solve for :
The solution to the equation is:
To verify, substitute back into the original equation:
The solution satisfies the original equation.
Would you like more details or have any questions?
Here are some related questions:
- How do you solve equations involving multiple square roots?
- What are the properties of square roots used in solving equations?
- Can you solve ?
- How do you verify solutions to square root equations?
- What are common mistakes to avoid when solving square root equations?
- How can you graph the function ?
- What is the domain of the function ?
- Can you solve ?
Tip: Always verify your solutions by substituting them back into the original equation to check if they satisfy the equation.
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Math Problem Analysis
Mathematical Concepts
Square Roots
Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12