If the sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

Let a, b be the two numbers.
.'. a + b = 7 and a3 + b3 = 133
(a + b)3 = a3 + b3 + 3ab (a + b)

⇒ (7)3 = 133 + 3ab (7)⇒ 343 = 133 + 21ab⇒  21ab = 343 - 133 = 210⇒ 21ab = 210

⇒ ab= 10

Now a2 + b2 = (a + b)2 - 2ab
                     = 72 - 2 x 10 = 49 - 20 = 29

Concept: Expansion of Formula

  Is there an error in this question or solution?