If x = root5-2 and y = root5+2 ; find (i) x square (ii) y square (iii) xy (iv) x square + y square + xy
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Answer:
Correct option is
A
323
We rationalize the denominator,
x=
5
+2
5
−2
×
5
−2
5
−2
x=
5−4
5+4−3
5
x=
1
9−4
5
.
Then, x
2
=(9−4
5
)(9−4
5
)
=81+16×5−72
5
=161−72
5
.
We rationalize the denominator,
y=
5
−2
5
+2
×
5
+2
5
+2
y=
5−4
5+4+4
5
y=
1
9+4
5
.
Then, y
2
=(9+4
5
)(9+4
5
)
=81+16×5+72
5
=161+72
5
.
Now, x=
5
−2
5
+2
and y=
5
+2
5
−2
.
Then, xy=
5
−2
5
+2
×
5
+2
5
−2
xy=1 .
Therefore, x
2
+y
2
+xy=161−72
5
+161+72
5
+1=323.
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