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