Question

if x^2+1/x^2=2 find x+1/x and x-1/x. Hence find also x^2 -1/x^2

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Answer 1

Step-by-step explanation:

Correct option is

A

-1

C

1

D

2

sin

−1

(x

2

+x+1)+cos

−1

(ax+1)=

2

π

cos

−1

(ax+1)=

2

π

−sin

−1

(x

2

+x+1)

cos

−1

(ax+1)=cos

−1

(x

2

+x+1)

x

2

+x+1−ax−1=0

x

2

+x(1−a)=0

x=

2

a−1±(1−a)

Therefore

x=0 and x=(a−1)

Also −1≤ax+1≤1

a

−2

≤x≤0

Clearly a cannot be 1 as we would get coincident values of x.

If a=-1, x=-2 then

cos

−1

(2+1)

cos

−1

(3) does not exists.

If a=2, x=1

sin

−1

(x

2

+x+1)

=sin

−1

(3)

Which does not exists.

Hence only a=0 and x=−1 satisfies the above equation.