The sum of two numbers is 16 and the sum of their squares 146. Find the two numbers.

With solution po please ​


Sagot :

Answer:

11 and 5

Step-by-step explanation:

Let x and y be the two numbers

First statement says "sum of two numbers is 16", so ...

[tex]x + y = 16[/tex]

and the second statement says "sum of their squares is 146", so ...

[tex] {x}^{2} + {y}^{2} = 146[/tex]

Using substitution method

[tex]x + y = 16 \\ y = 16 - x[/tex]

Substitute the y to 2nd equation

[tex] {x}^{2} + {y}^{2} = 146 \\ {x}^{2} + {(16 - x)}^{2} = 146 \\ {x}^{2} + 256 - 32x + {x}^{2} = 146 \\ 2 {x}^{2} - 32x + (256 - 146) = 0 \\ 2 {x}^{2} - 32x + 110 = 0[/tex]

[tex]{x}^{2} - 16x + 55 = 0 \\ (x - 11)(x - 5) = 0[/tex]

In this case, if ...

[tex]x - 11 = 0 \\ x = 11[/tex]

then

[tex]y = 16 - 11 \\ y = 5[/tex]

And if

[tex]x - 5 = 0 \\ x = 5[/tex]

then ...

[tex]y = 16 - 5 \\ y = 11[/tex]

So it means the two numbers are 11 and 5