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## Homework Statement

Hello , I need to find the real number solutions for the following equation.

[tex]\sqrt{a-x} + \sqrt{b-x} = \sqrt{a+b-2x}[/tex]

where [itex]b>a>0[/itex]

## Homework Equations

equation is given above

## The Attempt at a Solution

I squared both sides and and solved this. I got two solutions [itex]x=a[/itex] and [itex]x=b[/itex]. Now when we square both sides of the equations, there is possibility of getting some solutions which may not satisfy the original equation. Such solutions are called extraneous solutions. When I plug in [itex]x=a[/itex] in the original equations, LHS matches with the RHS. So its one of the solution which is a real number. But when I plug in the other possible solution [itex]x=b[/itex] in the original equation, I get the following [itex]\sqrt{a-b} = \sqrt{a-b}[/itex]. Now here left side matches with the right side. But since [itex]b>a>0[/itex], both sides are not real number anymore, So is [itex]x=b[/itex] extraneous solution or is it the second possible solution ?

thanks