Math (algebra)

posted by .

Let x and y be real numbers satisfying 4x^2+5y^2=1. Over all such pairs, let the maximum and minimum values of 2x^2+3xy+2y^2 be M and N respectively. If M+N+MN=a/b, where a and b are coprime positive integers, what is the value of a+b?

  • Math (algebra) -

    M = .789116
    N = .110884
    MN = .087500

    M+N+MN = .987500 = 79/80

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b , where a and b are coprime positive integers. …
  2. Math (Complex Numbers)

    Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
  3. Algebra

    Suppose that x and y are positive real numbers satisfying x^2 +y^2 =4xy . Then x−y/x+y can be written as ãa/b, where a and b are coprime positive integers. Find a+b .
  4. Mathematics

    Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1. The maximum possible value of x^3y^3+y^3z^3+z^3x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b?
  5. Maths

    Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1. The maximum possible value of x^3y^3+y^3z^3+z^3x^3 has the form ab where a and b are positive, coprime integers. What is the value of a+b?
  6. Please Help

    Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1. The maximum possible value of x^3*y^3+y^3*z^3+z^3*x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b?
  7. pllllls heeeeeeeeelp math

    Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1 . The maximum possible value of x^3*y^3+y^3*z^3+z^3*x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b ?
  8. heeeeeeeelp math

    Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1 . The maximum possible value of x^3*y^3+y^3*z^3+z^3*x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b ?
  9. Math (algebra)

    Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
  10. math

    If (x+2)f(2−x)+(2x+1)f(2+x)=1 for all real values of x, then f(18)=a/b, where a and b are coprime positive integers. What is the value of a+b?

More Similar Questions