1.

If (2x + 5y) = 12 and xy = 8, Find the value of 8x3 + 125y3 = ?1. -8522. -11523. 9544. -784

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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