Question
If a = 2 + √3, then the value of `(a^(6) +
a^(4) + a^(2) + 1)/(a^(3))` isSolution
a = 2 + √3 1/a = 1/(2 + √3) = 2 - √3 a + 1/a = 2 + √3 + 2 - √3 a + 1/a = 4 (a^6+a^4+a^2+1)/a^3 → (a^3 (a^3+a+1/a+1/a^3 ))/a^3 = a^3+a+1/a+1/a^3 = (a^3+1/a^3 ) + (a+1/a) a+1/a = 4 On cubing both sides, (a+1/a)^3 = (4)^3 a^3+1/a^3 + 3 × a×1/a (4) = 64 a^3+1/a^3 + 12 = 64 a^3+1/a^3 = 52 Therefore, a^3+1/a^3 + a+1/a = 52 + 4 = 56.
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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