Solve the equation (x-4)^1/2=1/(x-4).Solve the equation (x-4)^1/2=1/(x-4).  

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The equation to be solved is (x-4)^1/2=1/(x-4)

(x-4)^1/2=1/(x-4)

square both the sides

=> x - 4 = 1 / (x - 4)^2

=> (x - 4)^3 = 1

=> 1 - (x - 4)^3 = 0

=> (1 - (x - 4))(1 + x - 4 + (x - 4)^2) = 0

=> (1 - x + 4)(1 + x - 4 + x^2 + 16 - 8x) = 0

=> (-x + 5)(x^2 - 7x + 13) = 0

-x + 5 = 0

=> x = 5

x^2 - 7x + 13 = 0

=> x1 = 7/2 + sqrt(49 - 52) /2

=> x1 = 7/2 + i*(sqrt 3)/2

x2 = 7/2 - i*(sqrt 3/2)

The equation has the solutions x = (5, 7/2 + (sqrt 3)/2, 7/2 - (sqrt 3/2))

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial