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Question

If x=6+5, then x2+1x22=

A

26

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B

25

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C

24

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D

20

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Solution

The correct option is D (20)

Given x=6+5 ......(i)
Applying reciprocal property,
Then 1x=16+5=65(6+5)(65)

=65(6)2(5)2=6565

=651=
1x=65 ........(ii)

Now, consider x2+1x22=(x1x)2
[Since, (ab)2=a2+b22ab]

=[(6+5)(65)]2
[From equations (i) and (ii)]
=(6+56+5)2=(25)2
=4×5=20
Hence, the value of the given expression is 20.


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