Find three positive integers x, y, and z that satisfy the given conditions. the sum is 48, and the sum of the squares is a minimum.

Step-by-step explanation:

Given that x+y+z = 48

Sum of squares

is minimum

Let us eliminate one variable say z = 48-x-y

f(x,y) =

Use partial derivatives to find min of f

Equate I derivative to 0

2x+6y =96 and 6x+2y = 96

Solving we get

x=y =12

z=48-24 = 24

so minimum when x=y =12 and z = 24

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step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.