Question

If (x-1/x)=8,find the value of (x+1/x)​

Answer 1

Step-by-step explanation:

ANSWER IN ATTACHMENT FILE

Answer 2

Step-by-step explanation:

It is given that x−

x

1

=8, by squaring both sides we get:

(x−

x

1

)

2

=8

2

⇒(x)

2

+(

x

1

)

2

−(2×x×

x

1

)=64(∵(a−b)

2

=a

2

+b

2

−2ab)

⇒x

2

+

x

2

1

−2=64

⇒x

2

+

x

2

1

=64+2

⇒x

2

+

x

2

1

=66....(1)

Now, consider (x+

x

1

)

2

then we have:

(x+

x

1

)

2

=(x)

2

+(

x

1

)

2

+(2×x×

x

1

)(∵(a+b)

2

=a

2

+b

2

+2ab)

=x

2

+

x

2

1

+2

=66+2(Fromeqn1)

=68

⇒(x+

x

1

)

2

=68

⇒x+

x

1

=

68

⇒x+

x

1

=2

17

Now, consider the product of x−

x

1

and x+

x

1

as shown below:

(x−

x

1

)(x+

x

1

)=8×2

17

=16

17

⇒(x

2

−

x

2

1

)=16

17

(∵a

2

−b

2

=(a−b)(a+b))

Hence, (x+

x

1

)=2

17

and (x

2

−

x

2

1

)=16

17

.