Question

If a + b = 7 and a³ + b³ = 91, find the value of ab.

Answer 1

Here, a + b = 7 and a³ + b³ = 91.

Using the identity:

a³ + b³ = (a + b)³ − 3ab(a + b)

91 = (7)³ − 3ab(7)

91 = 343 − 21ab

21ab = 343 − 91

21ab = 252

ab = `52/21`

∴ ab = 12