Question

If 2x + y = 6 and xy = 4, then find the value of 8x³ + y³ is:

• A. 16
• B. 72
• C. 48
• D. 64

Answer 1

Answer:

B. 72

Solution:

Given:

2x + y = 6

xy = 4

Formula:

(x + y)² = x² + y² + 2xy

x³ + y³ = (x + y) (x² + y² - xy)

Calculation:

2x + y = 6

xy = 4

⇒ (2x + y)² = 4x² + y² + 4xy

⇒ 6² = 4x² + y² + 4 $\times$ 4

⇒ 4x² + y² = 36 - 16

⇒ 4x² + y² = 20

Now,

(2x)³ + y³ = (2x + y) (4x² + y² - 2xy)

⇒ 8x³ + y³ = 6 (20 - 2 $\times$ 4)

⇒ 8x³ + y³ = 6 $\times$ (20 - 8)

⇒ 8x³ + y³ = 6 $\times$ 12

∴ 8x³ + y³ = 72

Hence option (B) is correct answer.