Example 3.7.4: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares

The smallest possible value of the sum of their squares is 128.

Step-by-step explanation:

Let the first number = x

let the the second number = y

x +  y = 16

y = 16 -x

minimum value, f = x² + y²

f(x) = x² + (16-x)²

f(x) = x² + 256 - 32x + x²

f(x) = 2x² - 32x + 256

f(x)' = 4x - 32

4x - 32 = 0

4x = 32

x = 32 / 4

x = 8

The absolute minimum value of x = 8

y = 16 - x

y = 8

The smallest possible value of the sum of their squares is given by x² + y²;

=  (8)² + (8)²

= 128

Therefore, the smallest possible value of the sum of their squares is 128.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: