Question

Find two consecutive positive integers such that the sum of their squares is 761

Answer 1

`19^(2) +20^(2)` is 761

Explanation:

Answer 2

19 and 20

Explanation:

Let the integers be x and x + 1.

According to the question,

• x² + (x + 1)² = 761
• x² + x² + 2x + 1 = 761
• 2x² + 2x - 760 = 0
• x² + x - 380 = 0
• x² + 20x - 19x - 380 = 0
• x(x + 20) - 19(x + 20) = 0
• (x - 19)(x + 20) = 0
• x = 19, -20
• But x is a positive integer
• ⇒ x = 19

Therefore, the integers are :

• x = 19
• x + 1 = 20