WAEC Further Mathematics 2021 Theory question 103

Theory question 103

Surds

Given that (p + ½√3)(1 − √3)² = 3 − √3, find the value of p.

Show the model answer

Model answer

(1 − √3)² = 4 − 2√3.
p + ½√3 = (3 − √3)/(4 − 2√3) = (3 − √3)(4 + 2√3)/4 = (6 + 2√3)/4 = 3/2 + ½√3.
So p = 3/2.

Explanation

Rationalise the denominator, then compare.