Question
If (x + 6y) = 8, and xy = 2, where x > 0, what is the
value of (x3 + 216y³)?Solution
xy = 2 ⇒ y = 2/x .....(1) Also, (x + 6y) = 8 ⇒ x + (6 × 2/x) = 8 ⇒ x + 12/x = 8 .....(2) ⇒ (x + 12/x)3 = 83 [Taking cube of both sides] ⇒ x3 + (12/x)3 + 3 × x × (12/x) (x + 12/x) 512 ⇒ x3 + (12/x)3 + 3 × 12 × 8 = 512 [∵ We get from equation (2), x + 12/x = 8] ⇒ x3 + (12/x)3 + 288 = 512 ⇒ x3 + (12/x)3 = 512 - 288 ⇒ x3 + [(2 × 6)/x]3 = 224 ⇒ x3 + (6y)3 = 224 [∵ y = 2/x] ⇒ x3 + 216y3 = 224 ∴ The value of x3 + 216y3 is 224
Statements: Some oils are petrol.
                          All diesels are oils.
Conclusions: I. All die...
Statements:
Only a few Adidas are Nike
All Nike are Puma
No Nike is a Reebok
Conclusions:
I. All Puma being Nike...
In the question below there are three statements followed by two conclusions I and II. You have to take the three given statements to be true even if t...
Statements: Â Â Â Â Â Â Â Â Â All Meggi are momos.
                               All chowmin are momos.
...
Statements:
Some Branches are not Outlets.
Only a few Outlets are Stores.
All Stores are Camps.
Only a few Camps are Godown...
Statements:
Some kitchen is balcony.
No balcony is room.
Some room is floor.
All floor is roof.
Conclusions:
...Statements: Some Pulsar are not bajaj.
All bajajs are Hero.
Conclusions: I. Some bajaj are not Pulsar.
II. Some Heros are not baj...
Statements: Some pins are needles.
All needles are ropes.
Some ropes are buckets.
All buckets are trees.
Conclusions:I. some...
Statements:
All Composers are Professions.
Only a few Professions are Producers.
No Producer is Director.
Conclusions:
<...In the question below some statements are given followed by two conclusions I and II. You have to take the given statements to be true even if they see...