Question

(i) If x² + 1/x² = 7 and x ≠ 0; find the value of: 7x³ + 8x - 7/x³ - 8/x

Answer 1

Let x² + (1/x²) = 7 .................(1) 
Then, 

=( x² + 1/x² - 2.x.1/x ) = 7 - 2 

∴ ( x - 1/x )² = 5 

∴ x - 1/x = ± √5 .............. (2) 

∴ x³ - 1/x³ = ( x - 1/x )( x² + 1/x² + 1 ) 

. .. . . . . . .= ( ± √5 ) [ ( 7 ) + 1 ] ............. from (1), (2) 

. . . . . . . . .= ± 8√5 .................. (3) 

Hence, the required expression is 

= 7x³ + 8x - 7/x³ - 8x 

= 7 ( x³ - 1/x³ ) + 8 ( x - 1/x ) 

= 7 ( ± 8√5 ) + 8 ( ± √5 ) 

= ± ( 56 + 8 ) √5 

= ± 64√5  

Answer 2

Step-by-step explanation:

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