Which pair of numbers has a sum of 13 and whose squares differ by 65?
Show answer & explanation
Correct answer: C
Explanation
x + y = 13
x² − y² = 65
By the formula:
x² − y² = (x + y)(x − y)
65 = 13(x − y)
x − y = 5
x + y = 13
x − y = 5
⇒ 2x = 18 ⇒ x = 9
⇒ y = 4
9 and 4