math

posted by .

The sum of two numbers is 10.The sum of their squares is 52.Find the numbers.

  • math -

    one number --- x
    the other ---- 10-x
    x^2 + (10-x)^2 = 52
    x^2 + 100 - 20x + x^2 = 52
    2x^2 - 20x + 48 = 0
    x^2 - 10x + 24 = 0
    (x-6)(x-4) = 0
    x = 6 or x=4

    if one is 6, the other is 4
    if one is 4 the other is 6
    (symmetrical answers)

    the two numbers are 6 and 4

    check: 6+4 = 10
    36+16 = 52
    all is good!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calculus

    If the sum of two numbers is 1 and the sum of the cubes of the numbers is 3, what is the sum of the squares of the numbers?
  2. MATH

    The sum of the squares of two numbers is 2. The product of the two numbers is 1. Find the numbers. xy=1 x^2+y^2=2 x^4+1=2x^2 x^4-2x^2+1=0 I don't think you can factor that unless its (x^2+1)(x^2-1) but I don't know where to go from …
  3. Math

    Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
  4. Math 8th grade

    I NEED THESE IN ALGEBRAIC EXPRESSION!! The larger of two sums is 12 more than the smaller. Their sum is 84.Find the numbers. The sum of two numbers is 45. The first is 9 less than the second.Find the numbers. The second of two numbers …
  5. math URGENT!!!!

    i have a list of 5 different numbers. the sum of 2 of the numbers is 0. the sum of 2 of the numbers is 1. the sum of 2 of the numbers is 2. the sum of 2 of the numbers is 3. the sum of 2 of the numbers is 4.the sum of 2 of the numbers …
  6. Math

    A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
  7. math

    Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
  8. Math

    The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
  9. Perry

    The sum of two numbers is 15 the sum of the squares of the same two numbers is 172 fined the difference between the two numbers
  10. Math

    The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)

More Similar Questions