x 2 −5x+1=0 ∴x 2 +1=5x ∴x+ x 1 =5 ∴x 2 + x 2 1 =25−2=23 ∴x 3 + x 3 1 =(x+ x 1 ) 3 −3(x+ x 1 ) ∴x 3 + x 3 1 =125−15 ∴x 3 + x 3 1 =110 Now (x 3 + x 2 1 )(x 3 + x 3 1 )=56×23 ∴x 5 +x+ x 1 + x 5 1 =110×23 ∴x 5 + x 5 1 =2530−5 ∴x 5 + x 5 1 =2525. hope it will help you dear. Reply
x
2
−5x+1=0
∴x
2
+1=5x
∴x+
x
1
=5
∴x
2
+
x
2
1
=25−2=23
∴x
3
+
x
3
1
=(x+
x
1
)
3
−3(x+
x
1
)
∴x
3
+
x
3
1
=125−15
∴x
3
+
x
3
1
=110
Now (x
3
+
x
2
1
)(x
3
+
x
3
1
)=56×23
∴x
5
+x+
x
1
+
x
5
1
=110×23
∴x
5
+
x
5
1
=2530−5
∴x
5
+
x
5
1
=2525.
hope it will help you dear.