Math, asked by SaKriHa, 9 months ago

Given x+1/x =2,then x^4+1/x^4=?​

Answers

Answered by Hiteshbehera74
1

Answer: 2.

Formula used:

 {(x +  \frac{1}{x}) }^{2} =  {x}^{2}  +  \frac{1}{ {x}^{2} }  + 2

Attachments:
Answered by crownrohandeshpande
0

Step-by-step explanation:

As per the question, we have

x

+

1

x

=

11

(

x

+

1

x

)

2

=

(

11

)

2

... [Squaring both sides]

x

2

+

1

x

2

+

2

(

x

)

(

1

x

)

=

121

x

2

+

1

x

2

+

2

(

x

)

(

1

x

)

=

121

x

2

+

1

x

2

+

2

=

121

x

2

+

1

x

2

=

121

2

=

119

... (i)

Now, back to

x

+

1

x

=

11

(

x

+

1

x

)

4

=

(

11

)

4

x

4

+

1

x

4

+

4

(

x

3

)

(

1

x

)

+

6

(

x

2

)

(

1

x

2

)

+

4

(

x

)

(

1

x

3

)

=

(

11

)

4

x

4

+

1

x

4

+

4

(

x

2

)

+

6

+

4

(

1

x

2

)

=

14641

x

4

+

1

x

4

+

4

(

x

2

)

+

4

(

1

x

2

)

=

14641

6

x

4

+

1

x

4

+

4

(

x

2

+

1

x

2

)

=

14635

x

4

+

1

x

4

+

4

(

119

)

=

14635

... [Substituting the value of

x

2

+

1

x

2

from (i)]

x

4

+

1

x

4

+

476

=

14635

x

4

+

1

x

4

=

14635

476

x

4

+

1

x

4

=

14159

Hence, the answer.

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