Question

$x + 1 \div x = 3 \\ {x}^{5} + 1 \div {x}^{5} =$
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Answer 1

Given: x + 1/x = 3

To find: x⁵ + 1/x⁵ = ?

Step-by-step explanation :

Now, x² + 1/x² = (x + 1/x)² - 2 * x * 1/x

= 3² - 2

= 9 - 2

= 7

and x³+ 1/x³ = (x + 1/x)³ - 3 *x * 1/x * (x + 1/x)

= 3³ - 3 (3)

= 27 - 9

= 18

Here, (x² + 1/x²) (x³ + 1/x³)

= x⁵ + 1/x + x + 1/x⁵

= (x⁵ + 1/x⁵) + x + 1/x

or, x⁵ + 1/x⁵ = (x² + 1/x²) (x³ + 1/x³) - (x + 1/x)

= 7 * 18 - 3

= 126 - 3

= 123

Therefore, x⁵ + 1/x⁵ = 123