Question

x⁴+1/x⁴=47 find x³+1/x³​

Answer 1

Answer:

x⁴ + (1/x⁴) = 47

Adding and subtracting 2 on LHS,

x⁴ + (1/x⁴) + 2 - 2 = 47

[(x²)² + (1/x²)² + 2 × (1/x²) x²] = 47+2

( x² + 1/x² )² = 49

( x² + 1/x² )² = 7²

x² + 1/x² = 7 [neglecting the negative sign]

x² + 1/x² + 2 - 2 = 7

x² + 2.x².1/x² + 1/x² = 7+2

(x + 1/x)² = 9

(x+ 1/x)² = 3²

x + 1/x = 3 [neglecting the negative sign]

x³ + 1/x³ = (x+ 1/x)³ - 3.x.1/x(x + 1/x)

= (3)³ - 3(3)

= 27-9

= 18

Step-by-step explanation:

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