find the two numbers whose sum of the squares is a minimum if the product of the numbers is 10.

  1. 👍
  2. 👎
  3. 👁
  1. xy = 10, so y=10/x

    z = x^2+y^2 = x^2 + 100/x^2
    dz/dx = 2x - 200/x^3
    = (2x^2-200)/x^3

    dz/dx=0 when x=±10

    1. 👍
    2. 👎
  2. find two numbers whose product is 16 and whose sum of squares is minimum.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Find two numbers whose sum is 10 for which the sum of their squares is a minimum.

  2. calculus

    Find two positive numbers that satisfy the given requirements: The product is 147 and the sum of the first number plus three times the second number is minimum

  3. math

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

  4. MATH

    A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain

  1. Math

    Two numbers differ by 6. The sum of their squares is 116. Find the biggest number.

  2. Calculus

    Find the maximum and minimum product of 2 numbers who sum is 5

  3. Math (PLEASE HELP!)

    1. The sum of the squares of two numbers is 74 and the difference of their squares is 24. a) What system of equations models this situation? b) What are the two numbers? 2. For what value of b will the line y= -2x+b be tangent to

  4. calculus

    Find two numbers whose product is 16 and whose sum of squares is minimum

  1. Algebra 2

    What is the product of a complex conjugated? The product of complex conjugates is a difference of two squares it is always a real number. The product a complex conjugates may be written in standard form as a + bi where neither a

  2. mathematics

    Find two positive numbers whose product is 81 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.)

  3. Math

    1. If the product of 5 and the sum of 10 and a certain number is equal to 15, what is the number? 2. The sum of two consecutive counting numbers divided by their positive difference is 9. Find the larger numbers.

  4. math

    The sum of two positive numbers is 90. Find a function that models their product P in terms of x, one of the numbers.

You can view more similar questions or ask a new question.