# 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

## 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?

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