what are the two square numbers?
x² – y² = 21
(x + y)(x – y) = 21
There are two factor pairs of 21: 1·21 and 3·7
x ± y = 1, 21
or
x ± y = 3, 7
x – y = 1
x + y = 21
x = 11, y = 10
x² = 121, y² = 100
x – y = 3
x + y = 21
x = 12, y = 9
x² = 144, y² = 81
But 144 – 81 = 63 ≠ 21, eliminate this pair.
The two square numbers are 121 and 100
x² – y² = 21
(x + y)(x – y) = 21
There are two factor pairs of 21: 1·21 and 3·7
x ± y = 1, 21
or
x ± y = 3, 7
x – y = 1
x + y = 21
x = 11, y = 10
x² = 121, y² = 100
x – y = 3
x + y = 21
x = 12, y = 9
x² = 144, y² = 81
But 144 – 81 = 63 ≠ 21, eliminate this pair.
The two square numbers are 121 and 100
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