If x + y = 7 and x^3 + y^3 = 133 then xy=??

Question

If
x + y = 7 &
x^3 + y^3 = 133
Then
xy=??

Where x,y both are real numbers.

Answer 1

x is 5
y is 2
so xy=10

Answer 2

x^3 + y^3 = 133
(x+y)(x^2 + y^2 - xy) = 133
(7)(x^2 + y^2 - xy + 2xy - 2xy) = 133
(7)( (7*7) - 3xy ) = 133

343 - 21xy = 133
343 - 133 = 21xy
210 = 21xy
xy = 10

Ans :- 10

Answer 3

another way of solving is x^3+y^3=(x+y)(x^2-xy+y^2) substitute
133=7*(x^2+xy+y^2) or (x^2-xy+y^2)=19.........(1)
also (x+y)^2=x^2+2xy+y^2(i.e. 7^2)=49............(2)
subtract (1) from (2) leaving 3xy=30 or xy=10