Find the value of 27x 3 + 8y 3 , if 3x + 2y = 20 and xy = 11/9
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3x+2y=20
Cubing both sides,
(3x+2y)³=20³
or, (3x)³+(2y)³+3.3x.2y(3x+2y)=8000
or, 27x³+8y³+18xy(20)=8000 [∵, 3x+2y=20]
or, 27x³+8y³+18×11/9×20=8000 [∵, xy=11/9]
or, 27x³+8y³+2×220=8000
or, 27x³+8y³+440=8000
or, 27x³+8y³=8000-440
or, 27x³+8y³=7560
Cubing both sides,
(3x+2y)³=20³
or, (3x)³+(2y)³+3.3x.2y(3x+2y)=8000
or, 27x³+8y³+18xy(20)=8000 [∵, 3x+2y=20]
or, 27x³+8y³+18×11/9×20=8000 [∵, xy=11/9]
or, 27x³+8y³+2×220=8000
or, 27x³+8y³+440=8000
or, 27x³+8y³=8000-440
or, 27x³+8y³=7560
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