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.

(i) Let 2 numbers be x and y. The sum of the squares of two numbers is 13 and their product is 6. So,

x² + y² = 13

And,

xy = 6

Using the formula,

[∵ (x + y)² = x² + 2xy + y²]

(x + y)² = (x² + y²) + 2xy

Putting the value,

⇒ (x + y)² = 13 + 2 $\times$ 6

⇒ (x + y)² = 13 + 12

⇒ (x + y)² = 25

⇒ x + y = $\sqrt{25}$

⇒ x + y = 5 or -5

Hence, the sum of the two numbers = 5 or -5.

(ii) Using the formula,

[∵ (x - y)² = x² - 2xy + y²]

(x - y)² = (x² + y²) - 2xy

Putting the value,

⇒ (x - y)² = 13 - 2 $\times$ 6

⇒ (x - y)² = 13 - 12

⇒ (x - y)² = 1

⇒ x - y = $\sqrt{1}$

⇒ x - y = 1 or -1

Hence, the difference of the two numbers = 1 or -1.