Question

If x + ( 1/x ) = 2 , the value of x⁴ + (1/x⁴) is equal to

Answer 1

Answer:

ANSWER

x

4

+

x

4

1

=119

Adding 2 on both the sides,

x

4

+

x

4

1

+2=119+2

(x

2

+

x

2

1

)

2

=121⇒x

2

+

x

2

1

=11

Subtracting 2 on both sides.

x

2

+

x

2

1

−2=11−2

(x−

x

1

)

2

=9⇒x−

x

1

=±3

Hence, x−

x

1

=3.

Answer 2

AnwEr :

$\rightarrow \tt x + \dfrac{1}{x} = 2$

$\rightarrow \tt \bigg(x + \dfrac{1}{x} \bigg) ^{2} = 4 \\ \\ \rightarrow \tt {x}^{2} + \frac{1}{x {}^{2} } + 2 \cancel{x} \times \frac{1}{ \cancel{x}} = 4 \\ \\ \rightarrow \tt {x}^{2} + \frac{1}{ {x}^{2} } = 2$

Squaring again on both sides ,

$\rightarrow \tt \bigg( {x}^{2} + \dfrac{1}{ {x}^{2} } \bigg) ^{2} = 4 \\ \\\rightarrow \tt {x}^{4} + \frac{1}{ {x}^{4} } + 2 \cancel{x {}^{2} } \times \frac{1}{ \cancel{x}^{2} } = 4 \\ \\ \rightarrow \tt {x}^{4} + \frac{1}{ {x}^{4} } = 2$