if m=1+√2 then find the value of m^4 -1/m^4
Answers
Answered by
5
m^4 -1/m^4=(m^2 -1/m^2)(m^2 +1/m^2)
=(m -1/m)(m+1/m)(m^2 +1/m^2)
=(m -1/m)(m+1/m)[(m +1/m)^2-2] (1)
if m=1+√2
1/m=(1-√2)/(1-√2)(1+√2)=√2-1
(m +1/m)=2√2
(m -1/m)=2
from eq 1
m^4 -1/m^4=2*2√2*[(2√2)^2-2]
=4√2*6=24√2
=(m -1/m)(m+1/m)(m^2 +1/m^2)
=(m -1/m)(m+1/m)[(m +1/m)^2-2] (1)
if m=1+√2
1/m=(1-√2)/(1-√2)(1+√2)=√2-1
(m +1/m)=2√2
(m -1/m)=2
from eq 1
m^4 -1/m^4=2*2√2*[(2√2)^2-2]
=4√2*6=24√2
Similar questions