Question

How do you solve number 20?

Answer 1

We have

xy = 14 ⇔ x = 14/y

x + y = 30 ⇔ 14/y + y = 30

⇔ 14 + y² = 30y

⇔ y² - 30y + 14 = 0

Δ = b² - 4ac = (-30)² - 4 × 1 × 14 = 844 > 0

y = (-b ± √Δ) / (2a) = (30 ± √844)/2

xy = 14 ⇔ x × (30 ± √844)/2 = 14

⇔ x = 28/(30 ± √844)

So we have x - y = 28/(30 ± √844) - (30 ± √844)/2