If x+1/x=7, find x 2 +1/x 2 and x 4 +1/x 4
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If x+1/x = 7, then
x^2+1=7a or x^2-7a+1 = 0
Therefore, x = (7+/-sqrt(7^2-4*1*1))/2*1 = (7+/-sqrt(49-4))/2
Thus, x = (7+/-sqrt(45))/2 = (7+/-6.708)/2 = 13.708/2 or 0.584/2 = 6.854 or 0.292
Therefore, if x = 6.854, then x^2 + 1/x^2 = 6.854^2 + 1/6.854^2 = 46.977316 + 1/46.977316 = 47
and x^4 + 1/x^4 = 6.854^4 + 1/6.854^4 = 2206.8682 + 1/2206.868 = 2206.8686
x^2+1=7a or x^2-7a+1 = 0
Therefore, x = (7+/-sqrt(7^2-4*1*1))/2*1 = (7+/-sqrt(49-4))/2
Thus, x = (7+/-sqrt(45))/2 = (7+/-6.708)/2 = 13.708/2 or 0.584/2 = 6.854 or 0.292
Therefore, if x = 6.854, then x^2 + 1/x^2 = 6.854^2 + 1/6.854^2 = 46.977316 + 1/46.977316 = 47
and x^4 + 1/x^4 = 6.854^4 + 1/6.854^4 = 2206.8682 + 1/2206.868 = 2206.8686
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