31-01-2021
Mathematics

contestada

If x+2y=3 and xy=2 show that x³+8y³+9=0

Respuesta :

mhanifa mhanifa

31-01-2021

Step-by-step explanation:

Given

x + 2y = 3 and xy = 2
show that x³ + 8y³ + 9 = 0

Solution in steps:

(x + 2y)³ = 3³
x³ + 3x²(2y) + 3x(2y)² + (2y)³ = 27
x³ + 6x(xy) + 12y(xy) + 8y³ = 27
x³ + 8y³ + 6(x + 2y)xy = 27 ⇒ Substitute values
x³ + 8y³ + 6*3*2 = 27
x³ + 8y³ + 36 - 27 = 0
x³ + 8y³ + 9 = 0

Done

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