Math, asked by brainlymember14, 9 days ago

Need help with this problem

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Answers

Answered by BrainlyCul
0

Answer:

Given that, x=  

2

3−  

13

 

 

∴  

x

1

=  

3−  

13

 

2

           [Taking reciprocal on both sides]

We know that, (a+b)  

2

=a  

2

+b  

2

+2ab

∴ (x+  

x

1

)  

2

=x  

2

+  

x  

2

 

1

+2

⇒x  

2

+  

x  

2

 

1

=(x+  

x

1

)  

2

−2

Now, x+  

x

1

=  

2

3−  

13

 

+  

3−  

13

 

2

=  

2(3−  

13

)

(3−  

13

)  

2

+4

 

⇒  

2(3−  

13

)

9+13−6  

13

+4

=  

2(3−  

13

)

26−6  

13

 

 

⇒  

2(3−  

13

)

2  

13

(  

13

−3)

=  

2(3−  

13

)

−2  

13

(3−  

13

)

=−  

13

 

⇒ x+  

x

1

=−  

13

 

and hence, (x+  

x

1

)  

2

=(−  

13

)  

2

=13

∴ x  

2

+  

x  

2

 

1

=(x+  

x

1

)  

2

−2

⇒13−2=11

Hence, if x=  

2

3−  

13

 

, then the value of x  

2

+  

x  

2

 

1

 is 11.  

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