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
Directions : An idiom/phrase is given in bold. Following this idiom/phrase are given three sentences, which use the given idiom/phrase. The idiom/phras...
- Choose the option which best expresses the meaning of the idiom/phrase bold in the sentence.
Ravi is known to pull a fast one on his colleagues. In the following question, a sentence is given with the phrase or idiom highlighted in bold. Select the option given below that cannot replace the phra...
Dead Ringer
He had no intention of letting the Foreign Secretary steal any of his blunder .
Select the most appropriate meaning of the given idiom.
Pull up your socks
- Select the most appropriate option to substitute the underlined segment in the given sentence.
After months of hard work, the team finally achieved... Fill in the blank with an appropriate idiom.
The couple was __________, but they eventually got their act together.
Fill in the blanks with the correct idiom.
The new employee had no experience in the field, but he quickly adapted and showed that he was a ___...
Kiling of birds
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