Question

If x+y =4 and xy =2 then find x³ +y³

Answer 1

Answer:

Given, x−y=4 and xy=21 ...(i)

(x−y)

2

=4

2

⇒x

2

+y

2

−2xy=16

⇒x

2

+y

2

−2×21=16 (from (i))

⇒x

2

+y

2

=16+42=58

Now, x

3

−y

3

=(x−y)(x

2

+y

2

+xy)

=(4)(58+21)=316