If (54√2 x³ +24√3 y³)÷(√18 x + √12 y) = Ax² + By² + Cxy, then what is the value of A² - (B² + C²)?
If (54√2 x³ +24√3 y³) ÷ (√18 x + √12 y) = Ax² + By² + Cxy We know that, x³ + y³ = (x + y) (x² + y² - ab) => (54√2 x³ +24√3 y³) / (√18 x + √12 y) => [(√18 x + √12 y) (√18 x² + √12 y² - √18×12 xy)]/(√18 x + √12 y) => (√18 x² + √12 y² - √18×12 xy) => Ax² + By² + Cxy Now, => A = 18, B = 12 and C = -6√6 Putting value of A,B and C we get, => A² - (B² + C²) = 324 - (144 + 216) = -36
Statements: D % E, E & A, A @ B, B # C
Conclusions: I. C & AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. D # B
...Statements: L $ W, W * H, H # T, P % T
Conclusions: Â Â Â Â Â I. T @ L Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. H % LÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â...
Statements: F > G ≥ H; I ≥ J < H; J > K > L
Conclusions:
I. F > L
II. H ≥ K
III. G ≥ J
Which of the following letters should be placed in the blank spaces respectively (in the same order from left to right) to complete the given expression...
Statements: L > M = N > O, O > P ≥ T = R
Conclusion:
I. L > T
II. L ≥ R
Statements: R ≤ K ≤ H = O ≥ D > Q; K > P
Conclusions:I. K < Q II. D ≥ P
Statements: J ≤ K = L ≤ N; N ≤ O = M
Conclusions: I. M = JÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. J < M
...Statements: A % B & G @ T $ D; W % A # P
Conclusions :Â Â Â Â Â I. D % BÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. A % GÂ Â Â Â Â Â Â Â Â Â Â Â Â Â ...
Statements: Â Â Â Â Â Â Â Â Â S%R, R@U, U & V, V # N
Conclusions : Â Â Â Â Â Â Â Â Â
I. N @ U Â
II. R @ NÂ Â Â Â
...
Statements: V > I < Z > T = C ≥ A > G ≥ R
Conclusion
I: A < Z
II: C > R
