Math Problem Statement

Solve the nested square root expression involving constants: a = sqrt(3 - sqrt(6 - sqrt(10 + sqrt(15 + sqrt(21 - a)))))

Solution

The expression in the image is:

a=(3(6(10+(15+(21a)))))a = \sqrt{(3 - \sqrt{(6 - \sqrt{(10 + \sqrt{(15 + \sqrt{(21 - a)})})})})}

This is an equation where aa is defined in terms of itself through a nested square root expression. This type of equation is quite complex due to the recursive nature of aa. We can try to simplify or solve it by assuming a value for aa and verifying if it satisfies the equation, or we can attempt to find an analytical solution.

Solving the Equation:

To find a solution analytically, let's simplify the equation step by step.

  1. Assume aa is a specific value and substitute it into the expression.
  2. Simplify the expression and compare it to the assumed value.

However, solving this directly might be very complex analytically. A common approach to handle such equations involves iterative approximation

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Math Problem Analysis

Mathematical Concepts

Algebra
Recursive Expressions
Square Roots

Formulas

√(x)
Recursive Equations

Theorems

Square Root Properties
Recursion in Algebra

Suitable Grade Level

Grades 11-12