Question
Mozhan is thinking of two consecutive, odd perfect squares like (5^2 = 25 and 7^2 = 49). The difference between Mozhan's two squares is 80. What is the sum of Mozhan's two squares?
Answers
mathhelper
let the first odd number be x
then the next odd number is x+2
(x+2)^2 - x^2 = 80
x^2 + 4x + 4 - x^2 = 80
4x = 76
x = 19
so the consecutive squares are 19^2 and 21^2 or
361 and 441
their difference is 441-361 = 80
their sum is 441+361 = 802
then the next odd number is x+2
(x+2)^2 - x^2 = 80
x^2 + 4x + 4 - x^2 = 80
4x = 76
x = 19
so the consecutive squares are 19^2 and 21^2 or
361 and 441
their difference is 441-361 = 80
their sum is 441+361 = 802