the sum of the squares of two consecutive positive even numbers is 52. what is the smaller number

Question

translate this problem to an equation and solve

Answer 1

first even number =x

second even  number =x+2

 

x² +(x+2)²=52

 

x²+x²+4x+4=52

2x²+4x-48=0

x²+2x-24=0

(x+6)(x-4)=0

x=-6 and x=4

 

so smaller number = 4

larger number =6

 

 

 

Answer 2

x^2 + (x+2)^2 = 52

 

x^2 + x^2 + 4x + 4 = 52

 

2x^2 + 4x - 48 = 0

 

x^2 + 2x - 24 = 0

 

(  x   +   6 )( x   -     4  ) = 0

 

x + 6 = 0 ---> x = -6, which is not a positive integer.

 

x - 4 = 0 ---> x = 4

 

4 and 6, whose squares are 16 and 36 respectively, the sum of which is 52

 

4 and 6