The sum of two numbers is 11. The sum of their squares is 65. Find the numbers. (How do you get the answer?)

Well there is two different ways to find the answer there is the mathematical way( with an expression) or there is an easier way my way is the easy way

First, you find the numbers that add up to 11
1 + 10
2 + 9
3 + 8
and so on
then you have to square them
7 + 4 is the numbers that you are going to use for this question
7^2 =49
4^2 = 16
49 + 16 = 65
so your answer is 7^2 + 4^2 = 65

Answer Link

xero099 xero099 · Answer 2 · 2021-10-26T13:04:47+02:00

The numbers are 7 and 4.

In this question we need to translate the statement into an equivalent system of equations and solve the resulting system:

[tex]x + y = 11[/tex] (1)

[tex]x^{2} + y^{2} = 65[/tex] (2)

From (1):

[tex]x = (11-y)[/tex]

(1) in (2):

[tex](11-y)^{2}+y^{2} = 65[/tex]

[tex](121-22\cdot y +y^{2})+y^{2} = 65[/tex]

[tex]2\cdot y^{2}-22\cdot y +121 = 65[/tex]

[tex]2\cdot y^{2} - 22\cdot y +56 = 0[/tex]

We find all the roots of the resulting the second order polynomial by the quadratic formulas:

[tex]y_{1} = 7[/tex], [tex]y_{2} = 4[/tex]

By (1), we know the values for [tex]x[/tex]:

[tex]x_{1} = 4[/tex], [tex]x_{2} = 7[/tex]

The numbers are 7 and 4.

We kindly present to check this question on systems of equations: https://brainly.com/question/9351049