manna
Last Activity: 8 Years ago
x+1/x=4
and we need to find x^5+1/x^5
first of all to make a power of 5 weneed to cube it.
(x+1/x)^3=4^3
apply formula (a+b)^3=a^3+b^3+3ab(a+b)
x^3+1/x^3+3x*1/x(x+1/x)=64
x^3+1/x^3+3*4 =64 Because x+1/x=4 and x*1/x=1
x^3+1/x^3+12=64
x^3+1/x^3=52
now we need to do is
(x^3+1/x^3)^2=(52)^2
apply formula (a+b)^2=a^2+b^2+2ab
(x^3)^2+(1/x^3)^2+2x^3*1/x^3=2704
x^5+1/x^5+2=2704
x^5+1/x^5=2702---------hence answered