Question

if x to the power 4 + 1/x to the power 4 is equal to 47 find the value of x to the power 3 + 1/x to the power 3.​

Answer 1

x⁴ + 1/x⁴ = 47

Add 2 both sides :

= x⁴ + 1/x⁴ + 2 = 47 + 2

= x⁴ + 1/x⁴ + 2.x⁴.1/x⁴ + 2 = 49

Using ( a² + b² + 2 ab ) as ( a + b )²

= ( x² + 1/x² )² = 49

Take square root both sides

= x² + 1/x² = 7

Add 2 both sides again :

= x² + 1/x² + 2.x.1/x = 7 + 2

Using a² + b² + 2 ab = ( a + b )²

= ( x + 1/x )² = 9

Taking square root both sides

= x + 1/x = 3

Cube both sides

= ( x + 1/x )³ = 3³

= x³ + 1/x³ + 3 ( x + 1/x ) = 27

= x³ + 1/x³ + 3.3 = 27

= x³ + 1/x³ + 9 = 27

= x³ + 1/x³ = 27 - 9

= x³ + 1/x³ = 18

The value will be 18 .

Answer 2

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