Question

If x square+1/xsquare=7 find the value of x^3+1/x^3

Answer 1

Solution :

Given x² + 1/x² = 7

=> x² + 1/x² + 2•x•1/x=7+2

=> (x+1/x)² = 9

=> (x+1/x)² = 3²

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

Now ,

x³ + 1/x³

= (x+1/x)³ - 3(x+1/x)

= 3³ - 3×3

= 27 - 9

= 18

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