Question

If x+y=12,xy=27, then find x3-y3=?

Answer 1

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$\boxed{Hey}$

______________________________Given (x + y) = 12 and xy = 27 Recall, x3 + y3 = (x + y)3 – 3xy(x + y) ⇒ x3 + y3 = (12)3 – 3(27)(12) = 1728 – 972 ∴ x3 + y3 = 756

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Answer 2

Answer:

we know that , x^3-y^3=(x-y)(x^2+xy+y^2)

(x+y)^2=x^2+y^2+2xy

(12)^2=x^2+y^2+2(27)       [xy=27 given and x=y=12 given]

144=x^2+y^2+54

144-54=x^2+y^2

90 = x^2+y^2

also , using (x-y)^2=x^2+y^2-2xy

(x-y)^2=90-54

(x-y)^2=36

x-y= root of 36

x-y=6

therefore  (x-y)^2=(6)(90+27)

=(6)(117)

702

∴ x^3-y^3=702