Question

give example of two irrational number whose sum and product are rational

Answer 1

an example of two irrational numbers whose sum is a rational number


2 + 2 √ 2 = 3 √ 2, we have an example of two irrational numbers whose sum isan irrational number. 10. Give an example of two irrational numbers whose sum is a rational number

Answer 2

Example 1.)

( 1 + root2) and ( 1- root2)

Sum = 1 + root2 + 1 - root2

= 1 + 1

= 2

Product = ( 1 + root2) (1 - root2)

= 1^2 - (root2) ^2

= 1 - 2

= - 1

sum and product are rational

Example 2.)

( 5 - root3) and (5 + root3 )

Sum = 5 - root3 + 5 + root3

= 5 + 5

= 10

Product = ( 5 - root3) (5 + root3)

= 25 - 3

= 22