Are there two irrational numbers whose sum and product both are rationals? Justify.
Are there two irrational numbers whose sum and product both are rationals? Justify.
Yes,
$3+\sqrt{2}$ and $3-\sqrt{2}$ are two irrational numbers.
$(3+\sqrt{2})+(3-\sqrt{2})=6,$ a rational number.
$(3+\sqrt{2}) \times(3-\sqrt{2})=7,$ a rational number.
So, we have two irrational numbers whose sum and product both are rationals.
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