if x- y =4,and xy = -1 then the value of x^3 - y^3= ?,and x^3 + y^3= ?
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(x-y)^3=x^3-y^3-3xy(x-y)
(4)^3=x^3-y^3+3*4
64-12=x^3-y^3
x^3-y^3=52
we know that
(x-y)^2=x^2+y^2-2xy
16=x^2+y^2+2
x^2+y^2=14
to find x +y
(x +y)^2=x^2+y^2+2xy
(X+y)^2=14-2
(X+y)=√12
(X^3+y^3)=(x+y)(x^2-xy+y^2)
x^3+y^3=√12(14+1)
x^3+y^3=15√12
(4)^3=x^3-y^3+3*4
64-12=x^3-y^3
x^3-y^3=52
we know that
(x-y)^2=x^2+y^2-2xy
16=x^2+y^2+2
x^2+y^2=14
to find x +y
(x +y)^2=x^2+y^2+2xy
(X+y)^2=14-2
(X+y)=√12
(X^3+y^3)=(x+y)(x^2-xy+y^2)
x^3+y^3=√12(14+1)
x^3+y^3=15√12
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