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If 2x + 3y = (11)/(2) and xy = (5)/(6), ...

If `2x + 3y = (11)/(2) and xy = (5)/(6),` then the value of `8x ^(3) + 27 y ^(3)` is:

A

583

B

`(583)/(4)`

C

187

D

`(671)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
`2x + 3y = (11)/2 , xy = 5/6`
`implies (2x + 3y)^3 = ((11)/(2))^3`
`implies 8x^3 + 27 y^3 + 3(2x+3y) (2x xx 3y) = (1331)/(8)`
`implies 8x^3 + 27 y^3 + 3 xx (11)/(2) xx 6 xx 5/6 = (1331)/8`
`8x^3 + 27y^3 = (1331)/(8) - (165)/(2) = (1331-660)/(8)`
`implies 8x^3 + 27y^3 = (671)/(8)`
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