PYQ Vault
EbooksTutor

x and y reciprocal surd fractions (sqrt a +- sqrt b)/(sqrt a -+ sqrt b): use x + y and xy = 1

This type of question, asked 4 times: CDS 1 2018, CDS 1 2023, CDS 2 2025, CDS 1 2026. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2018

    18
    What is the value of 5−35+3−5+35−3\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}} - \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}?

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2023

    39
    If x=3+13−1x = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} and y=3−13+1y = \frac{\sqrt{3} - 1}{\sqrt{3} + 1}, then what is the value x3−y3x^3 - y^3 ?

    Tap an option to check your answer.

  3. Question 3

    CDS 2 2025

    28
    If p=5−25+2p=\frac{\sqrt{5}-2}{\sqrt{5}+2} and q=5+25−2q=\frac{\sqrt{5}+2}{\sqrt{5}-2}, then what is (pq+qp)\left(\frac{p}{q}+\frac{q}{p}\right) equal to?

    Tap an option to check your answer.

  4. Question 4 (case study, 2 parts)

    CDS 1 2026

    For the next two (02) items that follow : Let x=6+56−5x = \frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} - \sqrt{5}} and y=6−56+5y = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}
    85
    What is (x2−y2)\left(x^2 - y^2\right) equal to ?

    Tap an option to check your answer.

    86
    What is (x2−xy+y2)\left(x^2 - xy + y^2\right) equal to ?

    Tap an option to check your answer.