Expert: Paul Klarreich - 3/25/2006

Question
Hi Paul!  I'm actually taking Honors Trigonometry and Pre-Calculus this year (math has always been one of my strongest subjects), yet my math teacher keeps giving out "Challenge Problems" that seem to be more like Algebra.  Anyway, I keep getting 0% on them (as does the rest of the class) because they  make absolutely no sense, and even after the teacher explains them, they still make no sense.  It has lowered my grade from a 97.8% average to an 84%, so I'd greatly appreciate some help.  Here was last week's problem (which again, I got a zero on):

If X^2 + Y^2 = 15, and X * Y = 5, what is X + Y?

Well, I simply found the square root of 15 because if you take the square root of X^2 and Y^2, and you also take the square root of 15 (the other part of the equation), you're left with X + Y = 3.872983346.  That's the simply rules of algebra.  HOWEVER, this is what my teacher's solution was:

(X + Y)^2 = 15 + 5 * 2
(X + Y)^2 = 25
X + Y = 5

WHAT?  Where the heck does the "5 * 2" come from?  Please verify that I am not crazy!  I even went to another math teacher in the building and she said that my way was correct!  Do you see why my teacher would choose to solve it that way?  Thank you so much for any help!

Answer
Hi, Brittney,

You wrote:

Does this not make sense, or am I crazy???

>> Do you really want me to answer that?

Question:  Hi Paul! I'm actually taking Honors Trigonometry and Pre-Calculus this year (math has always been one of my strongest subjects), yet my math teacher keeps giving out "Challenge Problems" that seem to be more like Algebra. Anyway, I keep getting 0% on them (as does the rest of the class) because they make absolutely no sense, and even after the teacher explains them, they still make no sense. It has lowered my grade from a 97.8% average to an 84%, so I'd greatly appreciate some help. Here was last week's problem (which again, I got a zero on):

If X^2 + Y^2 = 15, and X * Y = 5, what is X + Y?

Well, I simply found the square root of 15 because if you take the square root of X^2 and Y^2, and you also take the square root of 15 (the other part of the equation), you're left with X + Y = 3.872983346.

>> NO, NO, NO!

That's the simply rules of algebra.

>> No, that's the WRONG rules of algebra.  The square root of  x^2 + y^2 is NOT  x + y.  Come on, now -- think about it:

Suppose  x = 4  and  y = 5.  Then x^2 + y^2 = 16 + 25 = 41.  But is it true that  4 + 5 = sqrt(41)?

HOWEVER, this is what my teacher's solution was:

(X + Y)^2 = 15 + 5 * 2
(X + Y)^2 = 25
X + Y = 5

WHAT??? Where the heck does the "5 * 2" come from? Please verify that I am not crazy! I even went to another math teacher in the building and she said that my way was correct!

>> That teacher should be fired, or reassigned to teach Spanish or History.  YOUR teacher is right.

Do you see why my teacher would choose to solve it that way? Thank you so much for any help!

-------------------------------
Sorry about that, but here is THIS teacher's solution:

x^2 + y^2 is not the same as (x + y)^2  [That's the point she was trying to make, of course. ]

Actually, (x + y)^2 = x^2 + y^2 + 2xy

And, since x^2 + y^2 is 15 and  xy is 5, then we have:

(x + y)^2 = 15 + 2(5) = 25

So x + y = 5  (actually, it's plus or minus 5)  

These look cute.  Send me some more.  And BEFORE you ask that other teacher.  Make sure you don't get his class next year.