Question

x²+1/x²=51 ; find x³-1/x³​

Answer 1

Answer:

Step-by-step explanation:

a  

3

−b  

3

=(a−b)(a  

2

+b  

2

+ab)

So,

x  

3

−  

x  

3

 

1

​  

=(x−  

x

1

​  

)(x  

2

+  

x  

2

 

1

​  

+x×  

x

1

​  

)

=(x−  

x

1

​  

)(x  

2

+  

x  

2

 

1

​  

+1)

=(x−  

x

1

​  

)(51+1)

=52(x−  

x

1

​  

)Now,

(x−  

x

1

​  

)  

2

=x  

2

+  

x  

2

 

1

​  

−2x×  

x

1

​  

 

(x−  

x

1

​  

)  

2

=51−2=49

x−  

x

1

​  

=  

49

​  

=7

Therefore,

x  

3

−  

x  

3

 

1

​  

=52(x−  

x

1

​  

)

=52×7