x^4+1/x^4=194 find x+1/x,x^3+1/x^3,x^2+1/x^2,x-1/x,x^3-1/x^3
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x^4 + 1 /x^4 = 194
(x ^2)^2 + 1 / ( x^2)^2 + 2 ( x^2) (1 /x^2)
-2 (x^2) (1 / x^2) = 194 .
(x^2 + 1 / x^2) ^2 - 2 = 194
(x^2 + 1 / x^2 ) ^2 = 196.
x^2 + 1 / x^2 = √196
x^2 + 1 / x^2 = 14
(x) ^2 + 1 / (x) ^2 + 2 (x) (1 /x) - 2(x) (1 /x) =14
(x + 1 / x )^2 - 2 = 14.
(x + 1/x )^2 =16
x + 1 / x = 4
hence, x + 1 /x = 4, x^2 + 1/ x^2 = 14.
now other terms you could find by yourself in the same manner.
hope it helps !
thank you !
(x ^2)^2 + 1 / ( x^2)^2 + 2 ( x^2) (1 /x^2)
-2 (x^2) (1 / x^2) = 194 .
(x^2 + 1 / x^2) ^2 - 2 = 194
(x^2 + 1 / x^2 ) ^2 = 196.
x^2 + 1 / x^2 = √196
x^2 + 1 / x^2 = 14
(x) ^2 + 1 / (x) ^2 + 2 (x) (1 /x) - 2(x) (1 /x) =14
(x + 1 / x )^2 - 2 = 14.
(x + 1/x )^2 =16
x + 1 / x = 4
hence, x + 1 /x = 4, x^2 + 1/ x^2 = 14.
now other terms you could find by yourself in the same manner.
hope it helps !
thank you !
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