Question
If x = 1 + √2 + √3 , then the value of (2x⁴ −
8x³ − 5x² + 26x − 28) is ?Solution
X = 1+ √2+√3 X -1 = √2+√3 both side squaring…. (x-1) ² = (√2+ √3) ² x²+ 1 - 2x = 5 + 2 √6 x² -2x = 4+2√6…… (1) both sides squaring…. (x² -2x-4) ² = (2√6) ² x⁴+ 4x² -4x³+16+16x-8x2 = 24 …. (2) x4-4x3-4x2+16x-8=0 multiply by 2. 2x4-8x3-8x2+32x-16=0 2x4-8x3-5x2+26x-28=3x2-6x-12 now – putting the value of equal. (1) and equal (2) =3(x-2x)-12 =3(4+2√6)-12 =12+6√6-12=6√6 After solving we will get it reduced to 6√6
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
