x+1/x=a then x^4+ 1/x^4= a^4-4a+2 prove it
Answers
Answered by
1
x+1/x=a
square on both sides,
(x^2 +1/x^2 +2(x*1/x) =a^2
x^2 +1/x^2 = a^2 -a
again square on both sides,
x^4 +1/x^4 +2(x^2 *1/x^2) = (a^2 -2)^2
x^4 +1/x^2 =(a^2 -2)^2 -2
x^4 +1/x^4 = a^4+ 4- 4a -2
x^4 +1/x^4=a^4 -4a+2
hence proved
square on both sides,
(x^2 +1/x^2 +2(x*1/x) =a^2
x^2 +1/x^2 = a^2 -a
again square on both sides,
x^4 +1/x^4 +2(x^2 *1/x^2) = (a^2 -2)^2
x^4 +1/x^2 =(a^2 -2)^2 -2
x^4 +1/x^4 = a^4+ 4- 4a -2
x^4 +1/x^4=a^4 -4a+2
hence proved
Similar questions