Question

Find whether x and y are rational or irrational in the following:

(i) a = 2 + √3, b = 2 – √3; x = a + b, y = a – b

(ii) a = √2 + 7, b = x = a + b, y = a – b

Answer 1

(i) Given that a = 2 + √3, b = 2 – √3

x = a + b = (2 + √3) + (2 – √3) = 4, a rational number.

y = a – b = (2 + √3) – (2 – √3) = 2√3, an irrational number.

(ii) Given that a = √2 + 7, b = √2 – 7

x = a + b = (√2 + 7) + (√2 – 7) = 2√2, an irrational number.

y = a – b = (√2 + 7 ) – (√2 – 7) = 14, a rational number.