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### Assignment 9

For which value(s) of is the line:

tangent to the graph of:

### Solution

First we try to find possible intersection points of and . Next we try to choose such that the intersection points coincide (or graphs have 'one' intersection point).

We find these intersection points of and from:

After squaring we find:

The solutions of this quadratic equations indicate the intersection points of and . The discriminant determines whether there are intersection points and if so, how many: 0, 1 or 2. We want that the graphs of and are tangent and thus :

so:

The value does not satisfy because a square root cannot take a negative value. Therefore the solution is:

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