Find the value of 27x3 + 8y, if 3x + 2y
7 and xy = 2
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Answer:
It is given that 3x+2y=12 and xy=6.
We find the value of 27x
3
+8y
3
as shown below:
27x
3
+8y
3
=(3x)
3
+(2y)
3
=(3x+2y)[(3x)
2
−(3x×2y)+(2y)
2
](∵a³+b³=(a+b)(a²−ab+b²))
=12[(3x)
2
−(6×xy)+(2y)
2
](∵3x+2y=12,xy=6)
=12[(3x)
2
−(6×6)+(2y)
2
]
=12[(3x)
2
−36+(2y)
2
]
=12[(3x)
2
+(2y)
2
+(2×3x×2y)−(2×3x×2y)−36]
=12[(3x+2y)
2
−12xy−36]
=12[(12)
2
−(12×6)−36]
=12(144−72−36)
=12(144−108)
=12×36
=432
Hence, 27x
3
+8y
3
=432.
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