Solve the equation square root(x^2-5)-square root(x^2-8)=1

Expert Answers

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

We have to solve sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

square both the sides

x^2 - 5 + x^2 - 8 - 2* sqrt [(x^2 - 5)(x^2 - 8)]  = 1

=> 2x^2 - 14 - 2* sqrt [(x^2 - 5)(x^2 - 8)]  = 0

=> x^2 - 7 = sqrt [(x^2 - 5)(x^2 - 8)]

square both the sides

=> x^4 + 49 - 14x^2 = x^4 - 13x^2 + 40

=> 9 - x^2 = 0

=> x^2 = 9

=> x = 3 and x = -3

The required solutions are x = 3 and x = -3

Approved by eNotes Editorial Team
Illustration of a paper plane soaring out of a book

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