Question

6) Two numbers have a sum of 15 and a product of 26. What are they?​

Answer 1

`\large \mathfrak{Solution : }`

let the numbers be x and y

now, we know that

• x + y = 15 - Equation (1)

• xy = 26 - Equation (2)

by squaring Equation (1) :

• (x + y)² = 15²

• x² + y² + 2xy = 225

• x² + y² - 2xy + 4xy = 225

• (x - y)² + (4 × 26) = 225

• (x - y)² + 104 = 225

• (x - y)² = 225 - 104

• (x - y)² = 121

• x - y = 11

• x = 11 + y - Equation (3)

Plugging the value of x from Equation (3) into Equation (1)

• x + y = 15

• 11 + y + y = 15

• 2y = 15 - 11

• y = 4 ÷ 2

• y = 2 - Equation (4)

now, let's plug the value of y from Equation (4) into Equation (3) :

• x = 11 + y

• x = 11 + 2

• x = 13

Answer 2

2 and 13

Explanation:

2+13=15

and

2x13=26