Question

If 3x +4y = 40 and xy = 5, find the value of 27x^3+ 64y^3

Answer 1

ANSWER:

Given:

• 3x + 4y = 40
• xy = 5

To Find:

• Value of 27x³ + 64y³

Solution:

We need to find the value of,

⇒ 27x³ + 64y³

We can write it as,

⇒ (3×3×3)x³ + (4×4×4)y³

⇒ (3)³(x³) + (4)³(y³)

⇒ (3x)³ + (4y)³

We know that,

⇒ a³ + b³ = (a + b)³ - 3(ab)(a + b)

So,

⇒ (3x)³ + (4y)³

⇒ (3x + 4y)³ - 4(3x × 4y)(3x + 4y)

⇒ (3x + 4y)³ - 4(12xy)(3x + 4y)

⇒ (3x + 4y)³ - 48xy(3x + 4y) -----(1)

We are given that,

• 3x + 4y = 40
• xy = 5

Substituting the value in (1),

⇒ (3x + 4y)³ - 48xy(3x + 4y)

⇒ (40)³ - 48(5)(40)

⇒ 64000 - 48(200)

⇒ 64000 - 9600

⇒ 54400

Hence, the value of 27x³ + 64y³ is 54400.