tmua.me Medium Set B Paper 2 · Question 9

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tmua.me Medium Set B Paper 2 · Q9

Paper 2Algebra

Let $a$ and $b$ be positive real numbers. Consider the conditions

P:\quad a+b\text{ is rational},\qquad Q:\quad a^2+b^2\text{ is rational}.

Which of the following is correct?

P

is sufficient but not necessary for

Q

P

is both necessary and sufficient for

Q

P

is neither necessary nor sufficient for

Q

P

is necessary but not sufficient for

Q

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