If the sum of squares of two real numbers is 41 and their sum is 9. Then the sum of cubes of these two numbers is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 189
Let the two number be a and b
a2 + b2 = 41
a + b = 9
So,
(a + b)2 = a2 + b2 + 2ab
⇒ 81 = 41 + 2ab
⇒ ab = 20
Now,
a3 + b3 = (a + b)[(a + b)2 - 3ab]
= 9(92 - 3 × 20)
= 9(81 - 60) = 189