Question

Find the value of ab and a² + b² in the following:

If a + b = 5 and a³ + b³ = 35

Answer 1

Here, a + b = 5, a³ + b³ = 35

Using the identity:

a³ + b³ = (a + b)³ − 3ab(a + b)

35 = 125 − 15ab

15ab = 125 − 35

15ab = 90

ab = `90/15`

∴ ab = 6

Now, 

a² + b² = (a + b)² − 2ab

= (5)² − 2(6)

= 25 − 12

∴ a² + b² = 13