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An equation x^2 -6x +18 = 0
The line y= 41 meets C at the point R.
Find the x-coordinates of R, giving you your answer in the form p + q(sqrt(2)), where p and q are integers.

I'm confused about this representation, I got -3 and 9 as the x coordinates yet I have no idea how to place it into this formula. The answer is 3 + 4(sqrt(2)) but I have no idea as to how to arrive at this. Do I use completed square form?

Respuesta :

This representation is fine for your purposes - no need to use the completed square form.

To arrive at this solution, you should set the expression (x^2-6x+18) equal to 41, and solve the resulting quadratic.  Subtract 41 from both sides to get x^2-6x-23, and from there, apply the quadratic formula to get:

[tex] \frac{6+-\sqrt{128}}{2} [/tex], or [tex]3+-4\sqrt{2} [/tex].  The line intersects the parabola at two points, [tex]3+4\sqrt{2}[/tex] and [tex]3-4\sqrt{2}[/tex].

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