x2-√3x+1=0 find x²+1/x²
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x^2 - 3x + 1 = 0, then it is possible to rewrite the equation like so.
x^2 = 3x -1 (Rearrange terms)
x = 3 - 1/x (Divide by x)
x + 1/x = 3 (Rearrange terms)
x^2 + 2 + 1/x^2 = 9 (square both sides)
x^2 + 1/x^2 = 7
When using the quadratic formula, x appears to be 3/2 + or - sqrt(5)/2, which doesn’t seem like it would generate a single value for x^2 + 1/x^2 at first glance.
Answer is 7+3=10
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