Question

X-y=4 et xy=21 calculer x^3-y^3

Answer 1

316 or -316.

Explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

= 4(x^2 + y^2 + 21)

x - y = 4

xy = 21

Substitute x = 4 + y in the last equation

(4 + y) y = 21

y^2 + 4y - 21 = 0

(y + 7)(y - 3) = 0

y = 3, -7.

So, x = 7, - 3.

So, x and y are 7 and 3 or -7 and -3.

But x^2 + y^2 = 9 + 49 = 58 whichever is true,

So, x^3 - y^3

= 4(x^2 + y^2 + 21)

= 4 (58 + 21)

= 316,

If x = -3 and y = -7 , then the answer is

-316.