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