Question

2) The sum of two numbers is 11 and sum of their squares is 61 find the numbers.​

Answer 1

$\Large \tt \fbox\red{Answér :}$

The numbers are 6 and 5.

As,

6 + 5 = 11

6^2 + 5^2 = 36 + 25 = 61

Answer 2

Answer:

I hope you find the solution helpful :)

Step-by-step explanation:

Given,

         Sum = 11

         Sum of squares = 61

Let the numbers be x and y.

So, x+y=11 or x=11-y

Also, given that x^2 + y^2 = 61

but, we know x=11-y

So, (11-y)^2 + y^2              = 61

     121 + y^2 + 22y + y^2 = 61

     2y^2 + 22y + 60         = 0

     y^2 + 11y + 30             = 0

     y^2 + 6y + 5y + 30     = 0

     y(y + 6) + 5(y + 6)       = 0

     (y+5)(y+6)                   = 0

So, y = -5 or -6.

And x = 16 or 17.

Therefore the numbers are either 16 and -5 or 17 and -6.