MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems
Problem
Consider the binomial expression a+bc, where a and b are rational numbers and c is a positive integer that is not a perfect square.
(i) Define the term "conjugate" of the binomial a+bc. Describe its form in one sentence.
(ii) Prove that the product of a binomial containing a square root and its conjugate is always a rational number by showing that (a+bc)(a−bc)=a2−b2c.
(iii) Using the result in part (ii), explain why the denominator becomes rational when the fraction 4+71 is multiplied by 4−7 both in the numerator and the denominator.