Question

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

Answer 1

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