Question

if (x+1/x)=6 find the value of (x-1/x) and (x^2-/x^2)​

Answer 1

→ Answer

$x+x1=6</p><p></p><p>⇒(x+x1)2=x2+x21+2x.x1</p><p></p><p>                           =x2+x21+2</p><p></p><p>⇒x2+x21=(x+x1)2−2=62−2=34</p><p></p><p>⇒(x2+x21)2=x4+x41+2x2.x21</p><p></p><p>                              =x4+x4+x41+2</p><p></p><p>⇒x2+x21=(x2+x21)2−2=342−2</p><p></p><p>                                                           =1154.</p><p></p><p>Hence, the answer is 1154.</p><p></p><p>$

Answer 2

Answer:

x+  

x

1

​  

=6

⇒(x+  

x

1

​  

)  

2

=x  

2

+  

x  

2

 

1

​  

+2x.  

x

1

​  

 

                          =x  

2

+  

x  

2

 

1

​  

+2

⇒x  

2

+  

x  

2

 

1

​  

=(x+  

x

1

​  

)  

2

−2=6  

2

−2=34

⇒(x  

2

+  

x  

2

 

1

​  

)  

2

=x  

4

+  

x  

4

 

1

​  

+2x  

2

.  

x  

2

 

1

​  

 

                             =x  

4

+x  

4

+  

x  

4

 

1

​  

+2

⇒x  

2

+  

x  

2

 

1

​  

=(x  

2

+  

x  

2

 

1

​  

)  

2

−2=34  

2

−2