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Algebra of Complex Numbers

If 2 x+3 y=13...

Question

If 2x+3y=13 and XY=6, find the value of 8x^3+27y^3 (question 6)

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Solution

2x +3y = 13-----(1)

xy =6-----(2)

8x³ +27y³ = (2x)³ +(3y)³

= (2x+3y)³ - 32x3y(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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