Question

x^4+1/x^4+1 factorise

Answer 1

Hi ,

x⁴ + 1/x⁴ + 1

= ( x² )² + ( 1/x² )² + 2 × x² × 1/x² - 1

= ( x² + 1/x² )² - 1²

= ( x² + 1/x² + 1 ) ( x² + 1/x² - 1 )

= [ x² + 1/x² + 2 - 1 ] [ x² + 1/x² - 1 ]

= [ ( x + 1/x )² - 1² ] [ x² + 1/x² - 1 ]


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

I hope this helps you.

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