Respuesta :

Americ
x= first number
x+2= second number

x^2 + (x + 2)^2= 100
square the parentheses

x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms

2x^2 + 4x + 4= 100
subtract 100 from both sides

2x^2 + 4x - 96= 0
factor

2(x−6)(x+8)=0
set each parentheses equal to 0

x-6= 0
x= 6

OR

x+8= 0
x= -8

CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100

x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100


ANSWER: x= 6 or x= -8

Hope this helps! :)

The numbers are 6 and -8

let

the first number = x

One of the number is 2 larger than another number .Therefore, the second number will be as follows;

  • x + 2

Sum of there squares will be as follows:

  • x² + (x + 2)² = 100

Therefore,

x² + x² + 4x + 4 = 100

2x² + 4x + 4 - 100 = 0

2x² + 4x - 96 = 0

x + 2x - 48 = 0

let's find x

x - 6x + 8x - 48 = 0

x(x - 6) + 8(x - 6) = 0

(x - 6)(x + 8) = 0

x -6 = 0 and x + 8 = 0

x = 6 and x = -8

The numbers are 6 and -8.

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