Math Problem Statement
Solve this
If a > 0 and x = 3 in the equation shown, what is the value of a? √(3a² - 3) - x = 0
Solution
The equation in the image is:
We are given and . Let's solve for .
Step 1: Substitute into the equation
Step 2: Add 3 to both sides
Step 3: Square both sides to eliminate the square root
Step 4: Add 3 to both sides
Step 5: Divide both sides by 3
Step 6: Take the square root of both sides
Since , the solution is .
Thus, the value of is 2.
Would you like further details or explanations on any step?
Here are 5 related questions to expand on this concept:
- How would the solution change if could be negative?
- What happens if you substitute instead of ?
- How would the problem change if the equation was ?
- Can you solve a similar equation where the square root is on both sides, like ?
- How do you solve for if the equation involved a cubic term, like ?
Tip: Always verify your solution by substituting the value of the variable back into the original equation to check for accuracy.
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Math Problem Analysis
Mathematical Concepts
Algebra
Square Roots
Solving Equations
Formulas
√(3a² - 3) - x = 0
a² = 4
Theorems
Properties of Square Roots
Suitable Grade Level
Grades 9-11