Question

\-x+sqrt1−x 2 \-=sqrt2(2x 2 −1). Solve for squrt.

Answer 1

Awnser

3

2

Explanation:

lim

x

→

1

√

x

−

√

2

−

x

2

2

x

−

√

2

+

2

x

2

√

x

−

√

2

−

x

2

2

x

−

√

2

+

2

x

2

⋅

√

x

+

√

2

−

x

2

2

x

+

√

2

+

2

x

2

=

x

−

2

+

x

2

4

x

2

−

2

−

2

x

2

=

(

x

+

2

)

(

x

−

1

)

2

(

x

+

1

)

(

x

−

1

)

=

1

2

(

x

+

2

x

+

1

)

and then

√

x

−

√

2

−

x

2

2

x

−

√

2

+

2

x

2

=

1

2

(

x

+

2

x

+

1

)

2

x

+

√

2

+

2

x

2

√

x

+

√

2

−

x

2

and then

lim

x

→

1

√

x

−

√

2

−

x

2

2

x

−

√

2

+

2

x

2

=

lim

x

→

1

1

2

(

x

+

2

x

+

1

)

2

x

+

√

2

+

2

x

2

√

x

+

√

2

−

x

2

=

1

2

⋅

3

2

⋅

4

2

=

3

2