Question 1128592
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Form a quadratic {{{highlight(cross(equations))}}} <U>equation</U> whose roots are 1+ sqrt2 and 1 - sqrt 2.
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Use the Vieta's theorem.



The product of the roots is the constant term of the polynomial:

    {{{(1+sqrt(2))*(1-sqrt(2))}}} = {{{1^2 - (sqrt(2))^2}}} = 1 - 2 = -1.



The sum of the root is equal to {{{(1+sqrt(2))*(1-sqrt(2))}}} = 2,

and it is the coefficient at x taken with the opposite sign.

Hence, the coefficient at x is equal to -2.



Then the equation is  {{{x^2 -2x -1}}} = 0.
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