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Mathematics

If 2x = 3y - 5, then find the value of 8x3 - 27y3 - 90xy + 125.

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Answer

Given, 2x = 3y - 5 or 2x - 3y = -5

Cubing both sides we get,

⇒ (2x - 3y)3 = (-5)3

(2x)3 - (3y)3 - 3(2x)(3y)(2x - 3y) = -125

⇒ 8x3 - 27y3 - 18xy(2x - 3y) = -125

⇒ 8x3 - 27y3 - 18xy(-5) = -125

⇒ 8x3 - 27y3 + 90xy = -125

⇒ 8x3 - 27y3 + 90xy + 125 = 0.

Hence, 8x3 - 27y3 + 90xy + 125 = 0.

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