If x=2+2√/3, x²+2/x²​

Answers 2

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If x=2+

3

then find the value of x

2

+

x

2

1

.

Easy

Solution

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x=2+

3

To find :x

2

+

x

2

1

Sol : x=2+

3

x

2

=(2+

3

)

2

=4+3+4

3

=7+4

3

x

1

=

2+

3

1

x

1

=

2−

3

2−

3

×

2+

3

1

x

1

=

4−3

2−

3

=

1

2−

3

(

x

1

)

2

=(2−

3

)

2

x

2

1

=4+3−4

3

=7−4

3

∴x

2

+

x

2

1

=7+4

3

+7−4

3

=14

∴x

2

+

x

2

1

=14

Solution:-

x=2+

3

To find :x

2

+

x

2

1

Sol : x=2+

3

x

2

=(2+

3

)

2

=4+3+4

3

=7+4

3

x

1

=

2+

3

1

x

1

=

2−

3

2−

3

×

2+

3

1

x

1

=

4−3

2−

3

=

1

2−

3

(

x

1

)

2

=(2−

3

)

2

x

2

1

=4+3−4

3

=7−4

3

∴x

2

+

x

2

1

=7+4

3

+7−4

3

=14

∴x

2

+

x

2

1

=14

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