Question
If [8(x + y)3 – 27(x – y)3] ÷
(5y – x) = Ax2 + Bxy + Cy2, then the value of (A2 - 2B + 3C) is:Solution
=> [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2 => [{2(x + y)}3 – {3(x – y)3}] ÷ (5y – x) = Ax2 + Bxy + Cy2 => {2(x + y)} – {3(x – y)}  [{2(x + y)}2 + 2(x + y)3(x – y) + {3(x – y)}2] ÷ (5y – x) = Ax2 + Bxy + Cy2 => (5y – x) [4x2 + 4y2 + 8xy + 6x2 – 6y2 + 9x2 + 9y2 – 18xy] ÷ (5y – x) = Ax2 + Bxy + Cy2 => 19x2 – 10xy + 7y2 = Ax2 + Bxy + Cy2 On comparing => A = 19, B = -10 and C = 7 => (A2 - 2B + 3C) = 192 - 2 × - 10 + 3 × 7 = 402
Statements: R ≥ T < U = V > W ≥ X, S < X > Y > Z
Conclusions:
I. U > S
II. T > Z
Statement: M < N ≤ O = P, Q ≥ O ≤ R ≤ Z
Conclusion: I. Q > MÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. Z > M
...Statements:
L ≥ M = N < P; O < Q ≥ R =S ≥ L
Conclusions:
I). Q > M
II). Q = N
Statements:
T % W % B $ I @ L
Conclusions:
I. B * T
II. L © B
III. L * T
Statements: C ≤ E ≥ F > D; A > I ≥ G ≥ E; H = L < A
Conclusions:
I. L = C
II. I ≥ F
III. A > D<...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 th...
Statements:
L ≤ J ≤ C = N; W ≥ X > L
Conclusions:
I. J ≤ X
II. X ˃ W
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 t...
Statement: C ≤ D < E; C > F > G
Conclusions: I. F < E II. C > G
...Statements: Q # N, N % S, S * U, U # M
Conclusions:
I. Q # S
II. Q * S
III. N % M
