Question
If (a + b + c) = 9, find (a – 4)3 + (b
– 2)3 + ( c – 3)3 - 3(a – 4 ) (b – 2 ) (c – 3)?Solution
a + b + c = 9 a + b + c = 4 + 2 + 3 (a – 4 ) + (b – 2) + (c – 3) = 0 If x + y + z = 0 x2 + y2 + z2 = 3xyz (a – 4)3 + (b – 2)3 + ( c – 3)3 = 3(a – 4 ) (b – 2 ) (c – 3) (a – 4)3 + (b – 2)3 + ( c – 3)3 - 3(a – 4 ) (b – 2 ) (c – 3) = 0
Statements:
P < Q < R < S ≤ B < H; S > N ≥ Y
Conclusions:
I) P < Y
II) R ≥ N
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and the...
Statements: P ≥ Q ≥ R = S, Q ≥ T > U ≥ V
Conclusion:
I. P ≥ V
II. P > V
Statements: J < K; L = M; K >N ≥ L
Conclusions:
I. J < L
II. N = M
Statements: M = N ≤ P = C > G, D ≥ M > T = F
Conclusion:
I. D ≥ N
II. N > F
III. F < P
Statements: A ≥ B ≥ Y = Z = M ≥ N ≤ E ≤ F = J
Conclusions:
I. F > Z
II. J ≤ Y
Which of the following expression symbols should replace the question mark(?) in the given expressions to make the expression C ≥ E as well as D > M d...
Statement: M < N; L ≥ U; L ≥ Q; U > N ≥ T
Conclusion:
I. N > Q
II. Q > T
Statements: X < H = U ≤ I < N = M, M > B ≥ V
Conclusions:
I. I > V
II. U ≥ MStatement: D > C > U < K > E > N < A
Conclusion:
I. D > N
II. D > A
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