If x-1/x=2 then find x^4+1/4^4
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x - 1/ x = 2
on squaring both side , we get
( x - 1/x )^2 = (2)^2
x^2 + 1/ x^2 - 2(x) (1/x) = 4
x^2 + 1/x^2 - 2 = 4
x^2 + 1/ x^2 = 6
again on squaring both side , we get
(x^2 + 1/x^2 )^2 = (6)^2
x^4 + 1/ x^4 + 2 (x^2 ) (1 /x^2) = 36
x^4 + 1 /x^4 + 2 = 36
x^4 + 1/x^4 = 36 - 2
x^4 + 1/ x^4 = 34
on squaring both side , we get
( x - 1/x )^2 = (2)^2
x^2 + 1/ x^2 - 2(x) (1/x) = 4
x^2 + 1/x^2 - 2 = 4
x^2 + 1/ x^2 = 6
again on squaring both side , we get
(x^2 + 1/x^2 )^2 = (6)^2
x^4 + 1/ x^4 + 2 (x^2 ) (1 /x^2) = 36
x^4 + 1 /x^4 + 2 = 36
x^4 + 1/x^4 = 36 - 2
x^4 + 1/ x^4 = 34
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