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Question -

If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 21y3.



Answer -

2x + 3y = 13, xy = 6
Cubing both sides,
(2x + 3y)3 = (13)3
⇒ (2x)3 +(3y)3 + 3 x 2x x 3X2x + 3y) = 2197
⇒ 8x3 +27y3 + 18xy(2x + 3y) = 2197
⇒ 8x3 +27y3 + 18 x 6 x 13 = 2197
⇒ 8X3 +27y3 + 1404 = 2197
⇒ 8x3 + 27y3 = 2197 – 1404 = 793
∴ 8x3 +27y3 = 793

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