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Question

If 2x+3y=10 and xy=2, the value of 8x3+27y3 is equal to

A
680
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B
640
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C
520
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D
740
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Solution

The correct option is B 640
It is given that 2x+3y=5
Using the identity we have
a3+b3=(a+b)33ab(a+b)
Taking a = 2x and b = 3y we get
(2x)3+(3y)3=(2x+3y)33(2x)(3y)(2x+3y)
8x3+27y3=(2x+3y)33(2x)(3y)(2x+3y)
8x3+27y3=1033(2x)(3y)(10)
8x3+27y3=1000180xy
8x3+27y3=1000180(2)
8x3+27y3=1000360
8x3+27y3=640









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