Friday, 15 May 2015

To Find The Roots Of the Given QUADRATIC EQUATIONS


5^(X+1)+5^(2-X)=5³ +1
 
5^X+5^1+5^2+5^-X=5³ +1
5^X+5 +25/5^X=126
PUT 5^X=Y.....(I)
Y+25/Y=126
5Y²-126Y+25=0
(Y-25)(5Y-1)=0
Y-25=0    OR   5Y-1=0
Y=25  OR Y=1/5
from (i)
5^X=25=5^2      5^X=1/5=5^(-1)
x=2                          x=(-1)
so -1 & 2 are the roots of the given equation