one positive number is 2 more than another. The sum of their squares is 34. Find the smaller number.

the numbers are 3 and 5

Step-by-step explanation:

x = first number

y = second number

a. x+2 = y

b. x^2 + y^2 = 34

Replace y from equation a into equation b:

x^2 + (x+2) ^2 = 34

Expand it

x^2 + x^2 + 4x + 4 = 34

2*x^2 + 4x = 30

2x^2 + 4x - 30=0

solving x:

x = - 5 and x = 3, it says it is a positive number, then it is x is 3

and the second number, y = x + 2

y = 5

Lets test it!

3^2 + 5^ 2 = 9 + 25 = 34

The smaller number is 3. The number 3 squared is 9, plus the other number 5 squared, which is 25. when you add them, you get 34