If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 27y3.

1.	If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 27y3.
Answer» Given: 2x + 3y = 13, xy = 6 Cubing 2x + 3y = 13 both sides, we get (2x + 3y)³ = (13)³ (2x)³ + (3y)³ + 3(2x )(3y) (2x + 3y) = 2197 8x³ + 27y³ + 18xy(2x + 3y) = 2197 8x³ + 27y³ + 18 x 6 x 13 = 2197 8x³ + 27y³ + 1404 = 2197 8x³ + 27y³ = 2197 – 1404 8x³ + 27y³ = 793

Answer»

Given: 2x + 3y = 13, xy = 6

Cubing 2x + 3y = 13 both sides, we get

(2x + 3y)³ = (13)³

(2x)³ + (3y)³ + 3(2x )(3y) (2x + 3y) = 2197

8x³ + 27y³ + 18xy(2x + 3y) = 2197

8x³ + 27y³ + 18 x 6 x 13 = 2197

8x³ + 27y³ + 1404 = 2197

8x³ + 27y³ = 2197 – 1404

8x³ + 27y³ = 793

Discussion

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