If x + 1/x = 4, find the values of
(i) x² + 1/x²
(ii) x⁴ + 1/x⁴
(iii) x³ + 1/x³
(iv) x - 1/x
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Step-by-step explanation:
It is given that , x + 1/x = 4 —( 1 )
Do the square of equation ( 1 ), ( x + 1/x )²
= 4² x² + 1/x² + 2
= 16 x² + 1/x²
= 16 – 2 x² + 1/x²
= 14 –( 2 )
Again do the square of equation ( 2 ),
( x² + 1/x² )²
= 14² x⁴ + 1/x⁴ + 2
= 196 x⁴ + 1/x⁴
= 196 – 2 = 194
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