Question

Me pueden ayudar no se me ocurre como resolverlo

Answer 1

x+y = 1
entonces:
x = 1-y

x² + y² = 2
(1-y)² + y² = 2
1-2y+y²+y² = 2
2y² - 2y +1-2 = 0
2y² - 2y -1 = 0

y = {2+-√(-2²) -(4*2*-1))} / 2*2
y = {2+-√(4+8)} / 4
y = {2+-√12} / 4
y = {2+-3.464} / 4
y₁ = {2-3.464} / 4 = -1.464/4 = -0.366
y₂ = {2+3.464} / 4 = 5.464/4 = 1.366

x₁ = 1-(-0.366) = 1+0.366 = 1.366
x₂ = 1-1.366 = -0.366

Entonces:
x₁³ + y₁³ = 1.366³ + (-0.366)³ = 1.366³ - 0.366³ = 2.549 - 0.049 = 2.5
x³ + y³ = -0.366³ +1.366³ = -0.049 + 2.549 = 2.5

Respuesta:
x³ + y³ = 2.5