Question 1144836
One number is five less than another.
a = b - 5
 The sum of their squares is 97.
a^2 + b^2 = 97
 Find the numbers.
replace a with (b-5)
(b-5)^2 + b^2 = 97
FOIL (b-5)(b-5)
b^2 - 5b - 5b + 25 + b^2 = 97
Combine like terms
2b^2 - 10b + 25 - 97 = 0
A quadratic equation
2b^2 - 10b - 72 = =
simplify, divide by 2
b^2 - 5b - 36 = 0
Factors to
(b - 9)(b + 4) = 0
the positive solution
b = 9
and
a = 9 - 5
a = = 4
:
The numbers are 9 & 4
:
However, b = -4, is another solution, therefore -9 and -4 can also be the numbers