Algebra

Subject: Algebra Thu Sep 04, 2008 8:12 am

Guys
Could you solve this one
If x^2-5x+1=0, then find the value of x^3+1/x^3

Active member

using long method

get x from dharacharya formula

you will get x=4.7912878474779195,0.20871215252208008

hence one value of x^3+1/x^3 is coming nearly 110

................

but i am sure that there must be some other easy method for this as in 10th calci. is not allowed.........

Subject: Solution of :- x^2-5*x+1=0 Sat Nov 15, 2008 9:49 pm

x^2-5*x+1=0
x(x-5)+1=0 {by taking x common}
x(x-5)=-1
x-5=-1/x
x+1/x=5
now cubing both sides,
(x+1/x)^3=5^3
x^3+1/x^3+3(x+1/x)=125 { By applying formula }
since,
x+1/x=5
therefore,
x^3+1/x^3+3*5=125
x^3+1/x^3+15=125
x^3+1/x^3=125-15
x^3+1/x^3=110
Hence,110 is the answer
By ,Tushar
Cool