If 2x - 3y = 10 and xy = 16, find the value of 8x 3 - 27y 3 .

Given, 2x - 3y = 10 Cubing both sides we get : ⇒ (2x - 3y) 3 = 10 3 ⇒ (2x) 3 - (3y) 3 - 3 × 2x × 3y(2x - 3y) = 1000 ⇒ 8x 3 - 27y 3 - 18xy(2x - 3y) = 1000 ⇒ 8x 3 - 27y 3 - 18 × 16 × 10 = 1000 ⇒ 8x 3 - 27y 3 - 2880 = 1000 ⇒ 8x 3 - 27y 3 = 3880. Hence, 8x 3 - 27y 3 = 3880.

Mathematics

If 2x - 3y = 10 and xy = 16, find the value of 8x³ - 27y³.

Expansions

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Answer

Given,

2x - 3y = 10

Cubing both sides we get :

⇒ (2x - 3y)³ = 10³

⇒ (2x)³ - (3y)³ - 3 × 2x × 3y(2x - 3y) = 1000

⇒ 8x³ - 27y³ - 18xy(2x - 3y) = 1000

⇒ 8x³ - 27y³ - 18 × 16 × 10 = 1000

⇒ 8x³ - 27y³ - 2880 = 1000

⇒ 8x³ - 27y³ = 3880.

Hence, 8x³ - 27y³ = 3880.

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If 2x - 3y = 10 and xy = 16, find the value of 8x³ - 27y³.

Expansions

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