Question

If 2a + 5b = 11, ab = 3, find the value of 8a³ +125b³.

Answer 1

Here, 2a + 5b = 11, ab = 3,

In the pattern of equation 2a + 5b we note that,

8a³ +125b³ = (2a)³ + (5b)³

Here, let x = 2a, b = 5b

Using the identity:

x³ + y³ = (x + y)³ − 3xy(x + y)

(2a)³ + (5b)³ = (2a + 5b)³ − 3(2a) (5b) (2a + 5b)

8a³ +125b³ = (11)³ − 3(10ab) (11)

8a³ +125b³ = (11)³ − 3[10(3)] (11)

8a³ +125b³ = (11)³ − 3(30) (11)

8a³ +125b³ = (11)³ − 3(330)

8a³ +125b³ = 1331 − 990

∴ 8a³ +125b³ = 341