Question

if 3x-2x=13 and xy=5 find the value of 27x^3 -8y^3

Answer 1

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Answer 2

here is your answer

GIVEN ➡ 3x - 2y = 13
and xy = 5

TO FIND ➡ 27x³ - 8y³
= [(3x)³ - (2y)³]

using identity a³ - b³ = (a-b)(a²+b²+ab)

= (3x-2y)[(3x)²+(2y)²-3x×2y]

= (3x-2y)(9x²+4y²-6xy). -(1)

ATQ

3x - 2y = 13

by squaring both sides

(3x - 2y)² = 13²

= (3x)² + (2y)² - 2×3x×2y = 169

= 9x² + 4y² - 12xy = 169

putting xy = 5 in equation

= 9x² + 4y² - 12×5 = 169

= 9x² + 4y² - 60 = 169

= 9x² + 4y² = 169 + 60 = 229

= 9x² + 4y² = 229

putting 9x² + 4y² = 229 in equation -(1)


(3x-2y)(9x² + 4y² - 6xy)

= 13 × (229 - 6×5)

= 13 × (229-30)

= 13 × 199

= 2587 is the answer

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