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

Question 143039: Solve

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

Add to both sides

Square both sides

Foil the right side

Subtract x from both sides. Subtract 1 from both sides

Combine like terms

Square both sides

Subtract 4x 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

However, we need to check our answers first

Check:
Let's check the solution

Start with the given equation

Plug in

Multiply

Add

Simplify the square roots

Subtract. So this verifies the solution

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

Now let's check the solution

Start with the given equation

Plug in

Multiply

Add

Simplify the square roots

Subtract. So this verifies the solution

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

Answer:

So the solutions are

or
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