Question

x ki power 4 + 1 upon x ki power 4 is equals to 194 find the value of x cube + 1 upon x cube or X square + 1 upon x square upon X + 1 upon x​

Answer 1

x⁴ + 1 / x⁴ = 194 ---( 1 )

( x² + 1 / x² )² - 2 = 194

( x² + 1 / x² )² = 194+2

x² + 1 /x² = √196

x² + 1 /x² = 14 -----( 2 )

( x + 1 / x )² - 2 = 14

( x + 1 / x )² = 14 +2

( x + 1/x ) =√16

x + 1 / x = 4------( 3 )

Therefore,

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

=4 × ( 14 - 1 )

[ From ( 2 ) and ( 3 )

= 4 × 13

= 52