Question

Give an example of two irrational numbers whose sum as well as product is rational

Answer 1

2+ root 2 and 2- root 2

sum is 4 and product is 2

Answer 2

Two irrational numbers whose sum and product are rational are 2+√5 and 2-√5.

VERIFICATION
I)
2+√5+(2-√5)
=2+√5+2-√5
=2+2
=4

II)
2+√5×(2-√5)
=(2)²-(√5)²
=4-5
=-1

Hence, proved