if x and y are positive integers and 2x + 3y = 13 and xy=6 then find 8x3 +27y3 what is the answer
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Given that,
2x + 3y = 13
Cubing on both sides,
(2x+3y)³=(13)³
We know that, (a+b)³=a³+b³+3ab(a+b)
So,
(2x)³+(3y)³+3(2x)(3y)(2x+3y) = 2197
8x³+27y³+18xy(2x+3y) = 2197
8x³+27y³+18(6)(13) = 2197 [ Replacing the values of xy and 2x+3y]
8x³+27y³+1404 = 2197
8x³+27y³ = 793
2x + 3y = 13
Cubing on both sides,
(2x+3y)³=(13)³
We know that, (a+b)³=a³+b³+3ab(a+b)
So,
(2x)³+(3y)³+3(2x)(3y)(2x+3y) = 2197
8x³+27y³+18xy(2x+3y) = 2197
8x³+27y³+18(6)(13) = 2197 [ Replacing the values of xy and 2x+3y]
8x³+27y³+1404 = 2197
8x³+27y³ = 793
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