For 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
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)
If 4pxy = (x + 2y)2 - (x - 2y)2, then what will be the value of p?
0.5
0.25
4
2
D.
2
4pxy = (x + 2y)2 - (x - 2y)2
⟹ 4pxy = (x + 2y + x - 2y) (x + 2y - x + 2y)
⟹ 4pxy = (2x) x (4y)
⟹ 4pxy = 8xy
⟹ p = 2