Multiple Choice QuestionsFor two positive numbers a and b, if a2 + b2 = 24 and ab = 6, then (a3 + b3) is equal to
96
10
102
102
If a, b, c are real numbers and a2 + b2 + c2 = 2(a - b - c) - 3, then the value of a + b + c is
-1
1
3
3
A.
-1
a2 + b2 + c2 = 2a - 2b - 2c - 3
⟹ a2 - 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⟹ (a - 1)2 + (b + 1)2 + (c + 1)2 = 0
⟹ a - 1 = 0, b + 1 = 0, c + 1 = 0
⟹ a = 1, b = -1, c = -1
∴ a + b + c = 1 - 1 - 1 = -1
If x + y + z = 6, then the value of (x - 1)3 + (y - 2)3 + (z - 3)3 is
3 (x - 1) (y - 2) (z - 3)
3xyz
(x - 1) (y - 2) (z - 3)
(x - 1) (y - 2) (z - 3)
and xy = 1, the value of 
is
and 
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