this is for the super smart people out their only people with a high IQ aloud?

Question

ok u redy












Is there a polynomial f(x,y) with real coefficients so that the set of values of the polynomial as x and y vary over the reals is the open interval (0, infinity)?

thanxx
for who ever answers my
question

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Answer 1

How about f(x, y) = x^2 + y^2 ?

Answer 2

f(x,y) = x^2 + y^2

is such a polynomial, however, it does include zero in its range, so its range is [0,infinity).

If you want to exclude 0, but get arbitrarily close to it, try this one (it's not a polynomial, however):

f(x,y) = e^(x + y)

Answer 3

yes