If 2a+3b=11 and ab=28,find 8a^3+27b^3
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2a+3b=11
Squaring both sides,
(2a+3b)²=(11)²
(2a)²+(3b)²+12ab=121
(2a)²+(3b)²+336= 121
(2a)²+(3b)²=121-336= -215
Now,
8a³+27b³= (2a)³+(3b)³
8a³+27b³= (2a+3b){(2a)²+(3b)²-ab}
8a³+27b³= (11) {-215+28}
8a³+27b³= 11 x (-187)
8a³+27b³= -2057
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