Question

n=√5-2\√5+2 and x=√5+2 \√5-2 : find 1.x² and 2.y²

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Answer 1

Answer:

We know, x 2+ x 21

=(x− x1 ) 2+2

Given, x=5−2 6

.Then, x1

= 5−2 61

= (5−2 6 )(5+2 6 )5+2 6

= 5 2 −(2 6) 2 5+2 6

= 25−245+2 6

= 15+2 6

=5+2 6

.Then, x 2 + x1

=(5−2 6 −(5+2 6 )) 2+2

∴(−4 6) 2+2=96+2=98.

Therefore, the required value is 98.