Let's set up the variables for the two numbers --> 'a' , 'b'
Now let's set up some equations based on the given information:
Equations:
Solve (equation 1) for b in terms of a
b = a - 6 -- equation 3
(equation 3) into (equation 2)
a^2 + (a - 6)^2 = 90
a^2 + a^2 - 12a + 36 = 90
2a^2 - 12a - 54 = 0
(2a + 6)(a - 9) = 0
a = -3 -- equation 4
a = 9 -- equation 5
(equation 4) into (equation 1)
-3 + b = 6
b = 9 - --- a = -3, b= 9
(equation 5) into ( equation 1)
9 + b = 6
b = -3 - --- a = 9, b= -3
Since the numbers are interchangeable, the two numbers are -3 and 9.
Hope it helps!
