Question

prove that x²+1/x² = (x-1/x)+2​

Answer 1

Answer:

The qn seems wrong. However making it correct trying to solve.

We know, a²+b²=(a-b)²+2ab

Using the same

LHS=x²+1/x²

      =(x-1/x)²+2.x.1/x

      =(x-1/x)²+2 = RHS

Step-by-step explanation:

Answer 2

Answer:

Here is your answer

Step-by-step explanation:

x

2

+x+1=0 implies

x=w,w

2

where w,w

2

are cube roots of unity.

Now

1+w+w

2

=0

w

3

=1

And

w

ˉ

=w

2

.

Now

(x+

x

1

)

2

+(x

2

+

x

2

1

)

2

....(x

27

+

x

27

1

)

2

=(w+

w

ˉ

)

2

+(w

2

+

w

2

ˉ

)

2

+...(w

27

+

w

27

ˉ

)

2

=(w+w

2

)

2

+(w

2

+w)

2

+(2)

2

+(w+w

2

)

2

+...(2)

2

=9(2

2

)+18(w+w

2

)

2

=36+18(−1)

2

=36+18

=54