Question

IF x+1/x = 4 then x^5 + 1/x^5 = ?

Answer 1

Answer:

x ×5+1/x×5

5x+1/5x

25x+1/5x

26x/5x

Answer 2

Given,
x+
x
1
​
=4......(1).
Now squaring both sides we get,
x
2
+2+
x
2

1
​
=16
or, x
2
+
x
2

1
​
=14.......(2).
Now again cubing equation (1) we get,
x
3
+3.x.
x
1
​
(x+
x
1
​
)+
x
3

1
​
=64
or, x
3
+
x
3

1
​
=64−12
or, x
3
+
x
3

1
​
=52.......(3).
Now multiplying (2) and (3) we get,
x
5
+x+
x
1
​
+
x
5

1
​
=728
or, x
5
+
x
5

1
​
=728−4=724. [ Using (1)].