Question

Daca puteti sa ma ajutati si la acest exercitiu va rog. Dau coroanaa!
Multumesc muuult!

Answer 1

x + y + z = 9

xy + yz + zx = 26

(x + y + z)(x + y + z) = x^2 + y^2 + z^2 + 2 (xy + yz + zx)

x^2 + y^2 + z^2 = (x + y + z)(x + y + z)  -  2 (xy + yz + zx) = 81 - 52 = 29

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x - y - z = 8

xy + xz - yz = -23

(x - y - z)(x - y - z) = x^2 - xy - xz -xy + y^2 + yz -zx + yz + z^2 = x^2 + y^2 + z^2 - 2xy - 2 xz + 2 yz = x^2 + y^2 + z^2 - 2(xy + xz - yz)

x^2 + y^2 + z^2 = (x - y - z)(x - y - z) + 2(xy + xz - yz) = 64 - 46 = 18

______________________

x + y + z = 25

x^2 + y^2 + z^2 = 327

x^2 + y^2 + z^2 = (x + y + z)(x + y + z)  -  2 (xy + yz + zx)

2(xy + yz + zx) = (x + y + z)(x + y + z) - (x^2 + y^2 + z^2) = 625 - 327 = 298

xy + yz + zx = 298/2 = 149

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x + y - z = 7

x^2 + y^2 + z^2 = 61

(x + y - z)(x + y - z) = x^2 + xy -xz +xy + y^2  - yz -zx -zy + z^2 = x^2 + y^2 + z^2 + 2xy - 2xz - 2yz = x^2 + y^2 + z^2 + 2(xy -xz - yz)

49 = 61 + 2(xy -xz - yz)

2(xy -xz - yz) = 49 - 61 = -12

xy -xz - yz = -6