Question

If x² +1/x² = 7 and x≠0 ; find the value of :7x² + 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 .............................. Ans.
.........................................

Happy To Help !