Question

If 3x + 4y = 40 and xy = 5, find the value of 27x3 + 64y3

Answer 1

Answer:

56800

Step-by-step explanation:

3x+4y = 40. (1)

xy = 5. (2)

Take cube both sides

Using the formula

(a+b)³ = a³ + b³ + 3ab(a+b)

(3x + 4y)³ = 40³

27x³ + 64y³ + 3*3x*4y*(3x+4y) = 64000

27x³ + 64y³ = 64000 - 36*xy*(3x+4y)

= 64000 - 36*5*40 [from (1) & (2)]

= 64000 - 7200 = 56800