Question

If
a+b= 9 and
ab=-2 find
a-b and a^2-b^2​

Answer 1

Answer:

Given:

a+b = 9

ab= -2

a-b = ?

a^2 - b^2 = ?

(a+b)^2 = a^2 + b^2 + 2 ab

or, (9)^2 = a^2 + b^2 + 2(-2)

or, 81 = a^2 + b^2 -4

or, a^2 +b^2 = 85

(a-b)^2 = a^2 + b^2 - 2ab

or, (a-b)^2 = 85 - 2(-2)

or, (a-b)^2 = 85 + 4

or, (a-b)^2 = 89

or, a- b = √89

a^2 - b^2 = ?

a^2 -b^2 = (a+b)(a-b)

or, a^2 -b^2 = (9)(√89)

or, a^2 -b^2 = 9√89