If x+1x=3 then, x7+1x7=?

Given:

x+1/x=3

To find:

x<sup>7</sup>+1/x<sup>7</sup>

Solution:

x+1/x=3

= x<sup>2</sup>+1/x<sup>2</sup>

= (x+1/x)<sup>2</sup>-2x(1/x)

= 3<sup>2</sup>-2

= 9-2

= 7

x<sup>3</sup>+1/x<sup>3</sup>

= (x+1/x)<sup>3</sup>-3x(1/x)(x+1/x)

= 3<sup>3</sup>-9

= 18

x<sup>4</sup>+1/x<sup>4</sup>

= 49

Therefore,

(x<sup>3</sup>+1/x<sup>3</sup>) (x<sup>4</sup>+1/x<sup>4</sup>) = 47.18

(x<sup>7</sup>+1/x<sup>7</sup>) = 843

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