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
Who was born on 12th April?
Which of the following boxes is placed immediately above and immediately below K?
Who among the following person celebrates on Friday?
Read the directions carefully and answer the following questions.
Five plays A, B, C, D and E are to be staged from Monday to Friday of a week....
Which of the following combination is correct?
Six persons R, S, T, U, V, and W live in a building of six-floors such that the bottommost floor is numbered as 1 and the topmost floor is numbered as ...
How many boxes are placed between Box A and Box B?
Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group?
...Which of the following is false?
What is the difference between the floor number of A and B?
Relevant for Exams:
