If x=(5-√21)/2 , find (x+1/x)²
Solve only 2 part
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If x=
2
5−
21
find (x+
x
1
)(x
2
+
x
2
1
)(x
3
+
x
3
1
)
Medium
Solution
verified
Verified by Toppr
x=
2
5−
21
x
1
=
5−
21
2
On stationalising denominator
x
1
=
5.
21
2
×
5+
21
5+
21
x
1
=
25−21
2(5+
21
=
2
5+
21
x+
x
1
=
2
5−
21
+
2
5+
21
⇒5
Now calculate x
2
+
x
2
1
(x+
x
1
)=5 square on both sides
x
2
+
x
2
1
+2=25
x
2
+
x
2
1
=23
⇒x
3
+
x
3
1
⇒(x+
x
1
)
3
=(5)
3
=x
3
+
x
3
1
+3(x+
x
1
)=125
=x
3
+
x
3
1
=110
Hence (x+
x
1
)(x
2
+
x
2
1
)+(x
3
+
x
3
1
)=5.23.110=12,650.
Answered by
1
Answer:
given x = 5-√21/2
to find = x² +1/x²
x² = (5-√21/2)²
25-21/4 = 4/4 = 1
now, 1/x² = 1/1 = 1
simple as that .... give me a thanks if it is helpful
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