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[ ( 0.8 )3 - ( 0.4 )3 ]/[ ( 0.8 )3 + ( 0.4 )3 ] = ?
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- 8/9
- 7/11
- 9/11
- 11/23
- 7/9
सही विकल्प: E
∵ [ ( 0.8 )3 - ( 0.4 )3 ]/[ ( 0.8 )3 + ( 0.4 )3 ] = ?
[ ∴ a3 - b3 = ( a - b )( a2 + ab + b2 तथा a3 + b3 = ( a + b )( a2 - ab + b2 ]
⇒ [ ( 0.8 )3 - ( 0.4 )3 ]/[ ( 0.8 )3 + ( 0.4 )3 ] = ( 0.8 - 0.4 )[ ( 0.8 )2 + ( 0.4 )2 + ( 0.8 × 0.4 ) ]/ ( 0.8 + 0.4 )[ ( 0.8 )2 + ( 0.4 )2 - ( 0.8 × 0.4 ) ]
= 0.4 × [ 0.64 + 0.16 + 0.32 ]/1.2 × [ 0.64 + 0.16 - 0.32 ] = ( 0.4 × 1.12 )/( 1.2 × 0.48 )
= ( 4 × 112 ) /( 12 × 48 ) = 448/576 = 14/18 = 7/9
∴ [ ( 0.8 )3 - ( 0.4 )3 ]/[ ( 0.8 )3 + ( 0.4 )3 ] = 7/9
∴ ? = 7/9
