Question

find the value of x^4+1/x^4 when x-1/x=5​

Answer 1

Step-by-step explanation:

Given, x−

x

1

=5

Squaring both sides,

(x−

x

1

)

2

=5

2

(x−

x

1

)

2

=25

⇒x

2

+

x

2

1

−2×x×

x

1

=25 .......... (a−b)

2

=a

2

−2ab+b

2

⇒x

2

+

x

2

1

−2=25

⇒x

2

+

x

2

1

=25+2=27

∴x

2

+

x

2

1

=27

Squaring both sides,

(x

2

+

x

2

1

)

2

=27

2

x

4

+

x

4

1

+2×x

2

×

x

2

1

=729 ............ (a+b)

2

=a

2

+2ab+b

2

x

4

+

x

4

1

+2=729

x

4

+

x

4

1

=729−2=727

∴x

4

+

x

4

1

=727

Answer 2

Answer:

$\huge{ \bold{ \boxed{ \pink{ \star{x - \frac{1}{x} = 5}}}}}$

$\huge{ \bold{ \boxed{ \blue{ \star{ {x}^{4} + \frac{1}{ {x}^{4} } = 527}}}}}$