Respuesta :
Answer:
The numbers at 13 and 13
Step-by-step explanation:
The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.
The two numbers are (13, 13).
Given that,
The sum of the two numbers is 26.
And the sum of their square is minimum.
We have to determine,
The two numbers are.
According to the question,
Let, the first number be x,
and the second number be y.
The sum of the two numbers is 26.
[tex]x + y = 26[/tex]
And The sum of their squares is a minimum.
[tex]x^2 + y^2 = h[/tex]
Solving both the equation,
[tex]x + y = 26\\\\x = 26-y[/tex]
Substitute the value of x in equation 2,
[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]
Then, The vertex of the parabola is,
[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]
The minimum value of the parabola is 13, which is also the sum of squares.
Therefore, The two number is x = 13 and y =13.
To know more about Parabola click the link given below.
https://brainly.com/question/4074088
