Question: Solve: $\sqrt{x} = 6 - \sqrt{x -24}$

Solution:
Given,

$\sqrt{x} = 6 - \sqrt{x -24}$

$or, \sqrt{x} + \sqrt{x -24} = 6$

$or, \sqrt{x -24} = 6 - \sqrt{x}$

[ Squaring both sides ]

$or, (\sqrt{x -24})^2 = (6 - \sqrt{x})^2$

$or, x -24 = 6^2 - 2×6×\sqrt{x} + (\sqrt{x})^2$

$or, x - 24 = 36 - 12\sqrt{x} + x$

$or, x - x +12 \sqrt{x} = 36 - 24$

$or, 12\sqrt{x} = 12$

$or, \sqrt{x} = \dfrac{12}{12}$

$or, \sqrt{x} = 1$

$or, \sqrt{x} = \sqrt{1}$

$\therefore x = 1$
= Answer