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If (2x + 5y) = 12 and xy = 8, Find the value of 8x3 + 125y3 = ?1. -8522. -11523. 9544. -784 |
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Answer» Correct Answer - Option 2 : -1152 Given: 2x + 5y = 12 xy = 8 Formula used: (a + b)2 = a2 + b2 + 2ab (a3 + b3) = (a + b) (a2 + b2 - ab) Calculations: 2x + 5y = 12 Both side square, (2x + 5y)2 = (12)2 ⇒ 4x2 + 25y2 + 20xy = 144 ⇒ 4x2 + 25y2 + 20 × 8 = 144 ⇒ 4x2 + 25y2 = -16 Now, 8x3 + 125y3 = (2x + 5y) (4x2 + 25y2 - 10xy) ⇒ (12) × (-16 - 10 × 8) ⇒ -1152 ∴ The value of 8x3 + 125y3 is -1152.
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