أوجد:أ^6 + ب^6 + جـ^6 إذا علمت:

so (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz
so xy + xz + yz = 3² - 9 = 0

x² + y² + z² - xy - xz - yz)(x + y + z) = x³ + y³ + z³ - 3xyz)
so 27 = 24 - 3xyz
so xyz = -1

(xy + xz + yz)² = x²y² + x²z² + y²z² + 2xyz(x + y + z)
so x²y² + x²z² + y²z² = 0 - 2(-1)(3) = 6

(x² + y² + z²)² = x^4 + y^4 + z^4 + 2x²y² + 2x²z² + 2y²z²)
so 81 = x^4 + y^4 + z^4 + 12
so x^4 + y^4 + z^4 = 69