Recent content by Euler_Euclid

  1. E

    Graduate Roots of x^3 + ax^2 + bx + c = 0

    If \alpha,\beta\ and\ \gamma are the roots of the eqn. (x-a)(x-b)(x-c)+1=0 then show that (\alpha-x)(\beta-x)(\gamma-x)+1=0
  2. E

    Graduate Find Perfect Square: Prime p & q Values

    please explain the whole solution. It was an Olympiad question and all of my friends couldn't do it.
  3. E

    Graduate Find Perfect Square: Prime p & q Values

    Find all values of p and q if p and q are prime numbers, p^2 + q^2 + 7pq is a perfect square.
  4. E

    Undergrad Solving for Real Values of x, y, & z with x+y=1 and xy-z^2=1

    find all real values such that: x+y=1 and xy-z^2=1 This one was in one of the exams we had.
  5. E

    Find Focal Length of Lens When Moving From 20cm to 15cm

    OK Sorry. I got it now! Thanks.
  6. E

    Find Focal Length of Lens When Moving From 20cm to 15cm

    Can you please help me a little more?
  7. E

    Find Focal Length of Lens When Moving From 20cm to 15cm

    If a lens is moved towards the object from a distance of 20cm to 15cm, the magnification of the image remains the same. What is the focal length of the lens? Sorry I am new here so please forgive me if I have violated any rules.:cry:
  8. E

    Graduate Proof: Fibonacci Sequence Sums to Squares

    Is there any other method other than this?
  9. E

    Graduate Proof: Fibonacci Sequence Sums to Squares

    not at all!
  10. E

    Graduate Proof: Fibonacci Sequence Sums to Squares

    if a_1, a_2, a_3 .... belong to the fibonacci sequence, prove that a_1a_2 + a_2a_3 + ... + a_{2n-1}a_{2n} = (a_{2n})^2