Math Problem Statement
Solution
This problem involves an infinite nested square root expression. To find the maximum value of , we can set the expression equal to a variable , and work with that.
Given the equation:
Step-by-Step Solution:
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Substitute the Nested Root: Since the square roots repeat infinitely, you can set the entire expression equal to :
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Square Both Sides: To eliminate the square root, square both sides of the equation:
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Rearrange the Equation: Now, solve for :
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Solve for when the expression is stable: At the stable value of the infinite nested square root, we want to be equal to the value inside the square root. Thus, substitute into the equation:
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Multiply by 4 to simplify:
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Factor the Equation:
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Math Problem Analysis
Mathematical Concepts
Infinite Series
Nested Square Roots
Algebra
Formulas
y = √(4x + y)
y^2 - y = 4x
y(y - 5) = 0
Theorems
Nested Radical Theorem
Suitable Grade Level
Grades 10-12