Question 197025
x^2  +1/x^2 = 4
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(x^4 +1) / x^2 =4
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x^4 +1 =4x^2
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x^4 -4x^2 +1 =0
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Let  y=x^2
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y^2 -4y +1 =0
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using  quadratic  eqn
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y = { -(-4) +/- sqrt (16-4)} / 2
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y = 2 +/- sqrt3
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but  y=x^2
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x^2 =2+/- sqrt3 =2+/- 1.732 = 3.732, .268
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x= 1.932, .518
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Returning  to  x^3 + 1/x^3 = ?
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1.932 ^3 + 1/ 1.932^3 = 7.35
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using  .518  gives  same  answer