Irrational makes rational? Or does it?

Number Theory Level 1

Do there exist two positive irrational numbers a a and b b such that both their sum and product are rational?

PART 2 of this problem

Yes No

Cantdo Math by CANTDO MATH , 16, Bangladesh

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3 solutions

Cantdo Math
May 8, 2020

The answer is Y E S \boxed{YES}

For example take a=3+ 2 \sqrt{2} and b=3- 2 \sqrt{2}

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Conjugate surds have both sum and product as rationals.

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Zakir Husain
Jun 2, 2020

Giving even a single example will solve, it my example: a = 2 , b = − 2 a=\sqrt{2},b=-\sqrt{2} a b = − 4 ab=-4 a + b = 0 a+b=0

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