Question

if x^4+1/x^4=194 then x^3+1/x^3=?

Answer 1

Hi ,

We know the identity ,
_______________________
a² + b² + 2ab = ( a + b )²

a² + b² = ( a + b )² - 2ab
________________________

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

I hope this helps you.

:)

Answer 2

Hi hope it will help u.. I have done the math in the most simple way...