Question

If x+1/x=5, then find the value of x^5+1/x^5​

Answer 1

Answer:

the value of x^5+1/x^5= 257/256.

Step-by-step explanation:

value of x= 1/4.

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Answer 2

Step-by-step explanation:

(x+1/x)=5

taking square on both sides

(x+1/x)²=5²

x²+2(x)(1/x)+1/x²=25

x²+2+1/x²=25

x²+1/x²=25-2

x²+1/x²=23

again taking square on both sides

(x²+1/x²)=23²

x⁴+1/x⁴+2(x²)(1/x²)=529

x⁴+1/x⁴+2=529

x⁴+1/x⁴=529-2

x⁴+1/x⁴=527

multiply both side with x+1/x

(x⁴+1/x⁴)(x+1/x)=527(x+1/x)

x⁵+(x⁴)(1/x)+x(1/x⁴)+1/x⁵=

x⁵+1/x⁵+x³+1/x³=

x⁵+1/x⁵=-x³-1/x³+527x+527/x