Question

The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.

Answer 1

Let x and y be the two numbers, then,

x² + y² = 13 and xy = 6

(i) (x + y)² = x² + y² + 2xy

= 13 + 2×6

= 13 + 12

= 25

∴ x + y = ± `sqrt25` = ±5

(ii) (x − y)² = x² + y² − 2xy

= 13 − 12

= 1

∴ x − y = ±1