Question number 1. How many solutions does the equation x minus 3 quantity squared plus y minus 2 quantity squared equal to 0 have? Rewriting our equation we see that on the right hand side there is a 0 so let me write it here on the left hand side and 0 here is obtained by adding together two quantities which are each squared. So if we square any number we cannot obtain a number that is less than 0. 0 is the smallest result of squaring for the first and for the second term and if we then add two numbers which are at least 0 and we expect 0 as the solution we know that here each term is in fact equal to 0 so x minus 3 quantity squared is equal to 0 provided x minus 3 is equal to 0 and that tells us that x is equal to 3 and then y minus 2 quantity squared is equal to 0 provided that we are squaring 0 so provided that y minus 2 is equal to 0 or that y is equal to positive 2. So then the solution that we have is a point and the point x comma y equal to 3 comma 2 is then the only solution so there is just one and we choose B as the correct answer.

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