SOLUTION: Solve. {{{sqrt(x-1)+sqrt(x-4)=sqrt(2x-1)}}}

Question 124675: Solve.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Square both sides

Square the right side to remove the square root

Foil the left side

Multiply

Foil

Combine like terms

Subtract 2x from both sides. Add 5 to both sides.

Combine like terms

Divide both sides by 2

Square both sides

Subtract 4 from both sides.

Factor the left side

Now set each factor equal to zero:
or

or Now solve for x in each case

So our possible answers are:
or

Check:
Let's verify the first solution

Start with the given equation

Plug in

Combine like terms

Simplify

Add. Since the two sides of the equation are not equal, this means that is not a solution.

-----------------

Let's verify the second solution

Start with the given equation

Plug in

Combine like terms

Take the square root

Add. Since the two sides of the equation are equal, this verifies the solution

So the only solution is
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