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If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3 + 216y3)?
- a)470
- b)368
- c)224
- d)288
Correct answer is option 'C'. Can you explain this answer?
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If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3+...
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If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3+...
Given:
(x + 6y) = 8
xy = 2
Formula used:
(a + b)3 = a3 + b3 + 3ab (a + b)
Calculation:
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
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If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3+ 216y3)?a)470b)368c)224d)288Correct answer is option 'C'. Can you explain this answer?
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