Question
If (54√2 x³ +24√3
y³)÷(√18 x + √12 y) = Ax² + By² + Cxy, then what is the value of A² - (B² + C²)?Solution
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
Statement: M>T≤Z; T>Q ; X ≥R>Q
I. X ≥ M
II. Q < M
Statements: Â P * R, M & N, R $ M
Conclusions:Â Â Â Â Â a) P @ MÂ Â Â Â Â Â Â Â Â Â Â Â Â b) P $ M
...In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and the...
Statement: B > C = J; B > S > E; B < N
Conclusion: I. E < C      II. J ≤ E
Statements:Â Â Â Â Â Â Â X @ Y % M % N; M $ P $ Z
Conclusions :     I. Y % Z               II. X @ N          �...
Statements: V ≤ R ≥ Q; R ≤ N < Y; I > Y ≤ S
Conclusions:
I. V ≤ S
II. I > Q
III. S > N
Statements: R % B, B & T, T @ E, E % G
Conclusions : I. T $ R II. R @ E III. B @ G
...Statement: H > G = M > S ; GÂ `>=` Â T > L; MÂ `<=` Â F <Â U
    Conclusion:  I. L > M          II. G < U
...How many such pairs of letter are there in the word TELEPHONE, each of which has as many letters between them in the word as in the English alphabet?
Statements: B > C; D > E = F < G ≥ H; C > I = D
Conclusions:
I. B < E
II. G > E
III. I < B
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