F asked in Science & MathematicsMathematics · 9 months ago

Find the general solution to the following equation. Give your answers as a number plus a multiple of π(don't approximate).sec^2(u)=2+sec(u)?

2 Answers

Relevance
  • 9 months ago

    sec^2u = 2 + secu

    sec^2u - secu - 2 = 0

    (secu - 2)(secu + 1) = 0

    secu = 2 or secu = -1

    u = pi/3 + 2npi or u = 5pi/3 + 2npi or u = pi + 2npi for all integers, n

  • ?
    Lv 7
    9 months ago

    Let s = sec(u). Rewrite as s²-s-2=0. Use the quadratic eqs or better yet, Factoring gives (s-2)(s+1)=0.

    Thus s = [left for you].

    Do that & we will take it from there if need be. 

    Ok, to your comment. The π/3 & 5π/3 are the primary solutions. They want ALL the solutions. That's why they asked you to write the answer with a free parameter like n. 

    The primary answers + 2πn  ( and +2πm) are all the solutions. 

    Don't forget to vote BA ! 

Still have questions? Get answers by asking now.