- #1
Faiq
- 348
- 16
Homework Statement
If a,b,c,d,e>1
then prove that
a^2/(c-1)+b^2/(d-1)+c^2/(e-1)+d^2/(a-1)+e^2/(b-1)=>20
The Attempt at a Solution
Given a,b,c,d,e are roots of a polynomial equation of a degree 5 then
x^2/(x-1)+x^2/(x-1)+x^2/(x-1)+x^2/(x-1)+x^2/(x-1)=>20
5 x^2/(x-1)=>20
x^2/(x-1)=>4
x^2=>4x-4
x=> 2
This proves that a,b,c,d,e >1
I am sure this method is wrong because I prove Q implies P rather than proving P implies Q. However I cannot work out any other method.