Question

if a/b + b/a = -1
a³ - b³ = ?​

Answer 1

Answer:

given

a/b + b/a = -1

(a^2 + b^2)/ab = -1

a^2 + b^2 = -ab

a^2 + ab + b^2 = 0

now

a^3 - b^3

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

= (a - b)*0

= 0

Answer 2

a/b + 1 = b/a

So,

a² + ab = -b²

a² + b² + ab = 0

Therefore,

a³ - b³

» ( a - b )( a² + b² + ab )

» ( a - b )( 0 )

» 0