a positive real number is 2 more than another.

Question

A positive real number is 2 more than another. If the sum of the squares of the two numbers is 16, find the numbers.

Answer 1

x² + (x+2)² = 16

 

x² + x² + 4x + 4 = 16

 

2x² + 4x - 12 = 0

 

x² + 2x - 6 = 0

 

x = [-2 ± √28] / 2 = [-2 ± 2√7] / 2

 

                            = 2(-1 ± √7)/2 = -1 ± √7

 

-1 - √7 is negative, so x = -1 + √7 and x+2 = 1 + √7

 

Answer 2

y = x + 2

 

x² + y² =16

 

x² +(x + 2)² = 16

 

x² + x² + 4x + 4 = 16

 

2x² + 4x = 12

 

x² + 2x = 6

 

complete the square

 

(x + 1)² = 6+1 = 7

 

x + 1 = √7  disregard -√7 because of stipulation in question

 

x = √7 - 1

 

and the other number is √7 + 1 (which is 2 more than √7 -1)