Question

If a - b = 10 and ab = 11; find a + b.

Answer 1

a - b = 10, ab = 11
We know that :
(a - b)² = a² - 2ab + b²
⇒ (10)² = a² + b² - 2 x 11
⇒ 100 = a² + b² - 22
⇒ a² + b²
= 100 + 22
= 122
Using (a + b)²  = a² + b² + 2ab, we get
(a + b)²
= 122 +2(11)
= 122 + 22
= 144
⇒ (a + b)
= `sqrt(144)`
= ±12.