can someone explain how to do this algebra problem? please help?

Question

Find 3 numbers in which the 1st is the sum of the 2nd and the 3rd, the 2nd is the square root of the 3rd and the sum of these 3 numbers is a minimum

Answer 1

let x = the 3rd number
Then sqrt(x) = 2nd number, and
x + sqrt(x) = 1st number
2x + 2sqrt(x) = S = sum of the three numbers
This function has a minimum value of 0 when x = 0. Its maximum value is + infinity.
Thus the only possible answer is 0 for each number.

Answer 2

Let the three numbers be A, B and C.
A = B + C
B = C^1/2
A + B + C = minimum

Let s =A + B + C

Substituting,
s= B + C + B + C
= 2(C^1/2 +C)

S = 2C^1/2 + 2C = min

To find the minimum value of the sum, differentiate s with respect to C and set the result equal to zero:

dS/dC = 1/C^1/2 + 2 = 0

1/C^1/2 = -2

C^1/2 = -1/2

C = 1/4
and
B = 1/2
A = 3/4

Answer 3

let a, b and c be three numbers.

a = b+c
b = sqrt(c)

minimize S = a +b +c

S = b +c +b +c = 2b +2c
S = 2sqrt(c) +2c
S = 2 (c +sqrt(c))
Find the derivative of S with respect to c

S ' = 1 + 1/(2sqrt(c)) =0

2sqrt(c) +1 =0
this has no solutions
min occurs when c =0
b =0 , a =0

Answer 4

Your question makes no sense. As a random guess:
1st: 6
2nd: 2
3rd: 4

This satisfies all the conditions, considering that the condition "the sum of these 3 numbers is a minimum" makes no sense.

Answer 5

(assuming non-zero values are needed, and no repeated numbers)
6 2 4 = 12

repeated numbers
2 1 1 = 4

zero's
0 0 0 = 0

Answer 6

F = S + T . .. equation 1 . . . S = F - T
S = √ T . . . . . equation 2 . . . substitute to 1
F = √ T + T
F + S + T = minimum value
if T =1 . . . F = 2 . . .S = 1 . . . . sum = 4