3. Prove that there exist infinitely many positive real numbers r such that the equation 2...

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3. Prove that there exist infinitely many positive real numbers r such that the equation 2 + 34 + 52 =r has no solution (r, y, z) EQx Qx Q. (Hint: Is the set S = {2" + 34 + 5 : (x, y, z) E Qx Qx Q} countable?) = r has no solution (x, y, z) € Q × Qx Q. 3. Prove that there exist infinitely many positive real numbers r such that the equation 2 + 34 + 52 =r has no solution (r, y, z) EQx Qx Q. (Hint: Is the set S = {2" + 34 + 5 : (x, y, z) E Qx Qx Q} countable?) = r has no solution (x, y, z) € Q × Qx Q.