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Question
If 2x+3y=13 and xy=6 find the value of 8x3+27y3.
If 2x+3y=13 and xy=6 find the value of 8x3+27y3.
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Solution
2x +3y = 13-----(1)
xy =6-----(2)
8x³ +27y³
= (2x)³ +(3y)³
= (2x+3y)³ - 3*2x*3y(2x+3y) [using (a+b)³ = a³+b³+3ab(a+b)]
= (13)³- 18 * 6 *13 [ using (1) and (2)]
= 2197 - 1404
=793
xy =6-----(2)
8x³ +27y³
= (2x)³ +(3y)³
= (2x+3y)³ - 3*2x*3y(2x+3y) [using (a+b)³ = a³+b³+3ab(a+b)]
= (13)³- 18 * 6 *13 [ using (1) and (2)]
= 2197 - 1404
=793
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