Question

Solve for X root X+1+root x-1=1

Answer 1

Answer:

X=5/4

Step-by-step explanation:

sqrt(x+1)-sqrt(x-1)=1

One solution was found :

x = (5/4)

Radical Equation entered :

√x+1-√x-1 = 1

Step by step solution :

Step 1 :

Isolate a square root on the left hand side :

Original equation

√x+1-√x-1 = 1

Isolate

√x+1 = √x-1+1

Step 2 :

Eliminate the radical on the left hand side :

Raise both sides to the second power

(√x+1)2 = (√x-1+1)2

After squaring

x+1 = x-1+1+2√x-1

Step 3 :

Get remaining radical by itself :

Current equation

x+1 = x-1+1+2√x-1

Isolate radical on the left hand side

-2√x-1 = -x-1+x-1+1

Tidy up

2√x-1 = 1

Step 4 :

Eliminate the radical on the left hand side :

Raise both sides to the second power

(2√x-1)2 = (1)2

After squaring

4x-4 = 1

Step 5 :

Solve the linear equation :

Rearranged equation

4x -5 = 0

Add 5 to both sides

4x = 5

Divide both sides by 4

A possible solution is :

x = (5/4)

Step 6 :

Check that the solution is correct :

Original equation, root isolated, after tidy up

√x+1 = √x-1+1

Plug in (5/4) for x

√(5/4)+1 = √(5/4)-1+1

Simplify

√2.25 = 1.5

Solution checks !!

Solution is:

x = (5/4)

One solution was found :

x = (5/4)