Question

x+1/x =5,find x3-1/y3​

Answer 1

Given, x−

x

1

=5

Squaring both the sides,

⇒(x−

x

1

)

2

=5

2

⇒x

2

+

x

2

1

−2(x)(

x

1

)=25

⇒x

2

+

x

2

1

=25+2

⇒x

2

+

x

2

1

=27

Now,

x

3

−

x

3

1

=(x−

x

1

)[(x)

2

+(

x

1

)

2

+(x)(

x

1

)]

=5(27+1)

=140

Answer 2

(x+1/x)=5

squaring both sides

(x+1x)²=25

(x-1/x)²+4=25

(x-1/x)²=21

x-1/x=√21

cubing both sides

(x-1/x)³=(√21)³

x³ - 1/x³ -3(x-1/x)=21√21

x³ - 1/x³ -3√21 = 21√21

x³ - 1/x³ =24√21