Question

If x + y = 9, xy = 20
find: x - y

Answer 1

x + y = 9, xy = 20
We know (a + b)
= a² + 2ab + b²
∴ (x + y)²
= 81 x² + y² + 2xy
⇒ x² + y²
= 81 - 2(120)
= 41
We also know (a - b)²
= a² - 2ab + b²
⇒ (x - y)²
= x² - 2xy + y²
⇒ (x - y)²
= 41 - 2(20)
= 1
⇒ x - y
= ±1.