Question

Solve for \( x \left( a \neq 0 \right) \) \[ \sqrt{(a + x)^2 + 4\sqrt{(a - x)^2}} = 5\sqrt{a^2 - x^2} \]

• A. \( x_1 = \frac{43}{45}a, x_2 = \frac{63}{65}a \)
• B. \( x_1 = \frac{43}{45}a, x_2 = 0 \)
• C. \( x_1 = \frac{63}{65}a, x_2 = 0 \)
• D. \( x_1 = \frac{63}{65}a, x_2 = 0 \)

Hint:

Always remember to simplify complicated square roots by first isolating variables and applying properties like distributive laws.

Answer 1

The Correct Option is C

This expression simplifies to \( x = \frac{63}{65} a \). The solution is deduced from the equation based on its symmetry and the properties of square roots.