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Find the sum of the xZ for which points on the parabola

y=x24x+7

lie below the line

y=x+6
Hint

You need to solve the inequality

x24x+7<x+6

Draw a sketch.

Solution

We need to solve the inequality

x24x+7<x+6x25x+1<0

The roots are

x=5±212x{0.209,4.79}

We should sketch the parabola y=x25x+1 to find the solutions

quadratic inequality

We see that the solution to the inequality is

0.209<x<4.79

and the integer solutions are x=1,2,3,4.