Question

Math Challenge!
If (x^3)-(y^3)=513 and xy=54 then prove (x-y)=3
Whoever can solve it will get 30 thanks and i'll follow him/her.
I've solved it in 30 min​

Answer 1

x³-y³=(x-y)(x²+y²+xy)

513=(x-y)(x²+y²+54)

513=(x-y)((x-y)²+2xy+54)

513=(x-y)((x-y)²+162)

if you put x-y=3 in this

you will get lhs=rhs

Answer 2

Answer:

let us assume

x=9,y=6

(x^3)-(y^3)=513

(9^3)-(6^3)=513

xy=54

(9)(6)=54

therefore..

(x-y)=3

(9-6)=3...

hope it's correct