Question

If x+1/x = 4
Find x⁵+1/x⁵​

Answer 1

Answer:

$\huge\mathfrak\pink{Answer:-}$

$your \: answer \: will \: be \: 724$

Answer 2

Step-by-step explanation:

x+1/x=5 …(i)

Squaring both sides

x²+1/x² +2=5²

x²+1/x² =23 …(ii)

Again squaring both sides

x⁴+1/x⁴ +2=23²

x⁴+1/x⁴ =23²-2=529-2=527 …(iii)

Multiplying (i) and (iii) we get

(x⁵+1/x⁵ )+(x³+1/x³ )=527×5=2635

i.e.

(x⁵+1/x⁵ ) =2635 - (x³+1/x³ ) …(iv)

To get the value of (x³+1/x³ )

Multiply (i) & (ii)

(x³+1/x³ )+(x+1/x)=23×5=115

i.e. x³+1/x³ =115-5=110

Putting this value in (iv)

We get

x⁵ + 1/x⁵ =2635-110=2525 which is required answer.