x^(3/2) - 14x^(1/2) + 49x^(-1/2) = 0

Question

find all real solutions.

Answer 1

Multiply by √x to get x² - 14x + 49=0.

 

This new equation then factors as (x-7)² = 0

 

Therefore the solution is x=7

 

You can easily verify that this solution is not extraneous.

Answer 2

x^3/2 - 14x^1/2 + 49/x^1/2 = 0

 

Multiply both sides by x^1/2:  x² - 14x + 49 = 0

 

                                        (x - 7)² = 0

 

                                                x = 7