Math, asked by Vectooki4028, 1 month ago

2+13 square/2-13 square= x and 2-13 square/2+13 square= y find the value of x square and y square

Answers

Answered by ayeda41
0

Answer:

Given that, x=

2

3−

13

x

1

=

3−

13

2

[Taking reciprocal on both sides]

We know that, (a+b)

2

=a

2

+b

2

+2ab

∴ (x+

x

1

)

2

=x

2

+

x

2

1

+2

⇒x

2

+

x

2

1

=(x+

x

1

)

2

−2

Now, x+

x

1

=

2

3−

13

+

3−

13

2

=

2(3−

13

)

(3−

13

)

2

+4

2(3−

13

)

9+13−6

13

+4

=

2(3−

13

)

26−6

13

2(3−

13

)

2

13

(

13

−3)

=

2(3−

13

)

−2

13

(3−

13

)

=−

13

⇒ x+

x

1

=−

13

and hence, (x+

x

1

)

2

=(−

13

)

2

=13

∴ x

2

+

x

2

1

=(x+

x

1

)

2

−2

⇒13−2=11

Hence, if x=

2

3−

13

, then the value of x

2

+

x

2

1

is 11.

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