Question
Solution
As we know, (x3 + y3) = (x + y) (x2 + y2 - xy) (x3 – y3) = (x - y) (x2 + y2 + xy) (x + y)2 - (x - y)2 = 4xy [(x - y)2 + 3xy] = [x2 + y2 - 2xy + 3xy] = [x2 + y2 + xy] [(x + y)2 - 3xy] = [x2 + y2 + 2xy - 3xy] = [x2 + y2 - xy] Now- (x3-y3)/x[(x+y)2-3xy] ÷y(x-y)2+3xy]/ x3+y3 ×(x+y)2-(x-y)2 /x2- y2 = (x - y) (x2 + y2 + xy)/x [x2 + y2 - xy] ÷ y [x2 + y2 + xy]/ (x + y) (x2 + y2 - xy) × 4xy/(x-y) (x+y) = (x - y) (x2 + y2 + xy)/x [x2 + y2 - xy] × (x + y) (x2 + y2 - xy)/ y [x2 + y2 + xy] × 4xy/(x-y) (x+y) =4
Read the given statement and conclusions carefully. Decide which of the given conclusions is/are true based on the statement.
Statement:
U...
Statements: U $ N © C @ H © Y
Conclusions:Â
 I. U © HÂ
II. C # UÂ
III.H © U
Statements: D > E > G ≤ H < I; G > P > F
Conclusions:
I. D > F
II. P < I
III. D > I
If '>' denotes '+', '<' denotes '-', '-' denotes '×', '×' denotes '÷', '÷' denotes '=', then choose the correct statement of the following.
...Statements: Z ≤ O = Q < P; A = X > M = Y ≥ P
Conclusions:
I. A > O
II. Z < X
III. Q ≤ M
Statement: A < B; D ≤ C = B; I > C; E ≥ B
Conclusion:
I. I > E
II. E ≥ I
Statements: S > U ≥ V = X, Y < M < X, Y = T ≥ W
Conclusions:
I. S > Y
II. M ≤ U
III. W < XStatement: C ≥ O ≥ S = Z ≤ N = R
Conclusions:
I. C > N
II. S ≤ R
Statements: Z % Y; X # W; U % V; W & V; Y @ X
Conclusions:Â Â Â Â Â
I. U @ X Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...
Statements: B & A, A # O, O $ Z, Z @ S
Conclusions:
I. Z $ A
II. Z & A