(3 + root(a))(4 + root(a)) = 17 + k(root(a)) where a and k are positive integers. Find the value of a and the value of k.

Let's open out the bracket using the FOIL method (first, outside, inside, last):

(3 + root(a))(4 + root(a)) = 12 + 3root(a) + 4root(a) + (root(a))2 = 12 + 7root(a) + a.

Since the answer 17 + k(root(a)) is in the form of an integer + surd, we must equate the integers and surds of 12 + 7root(a) + a     with       17 + k(root(a)).

Therefore, 12 + a = 17       so     a = 5

7root(a) = k(root(a))           so     k = 7.

Answered by Abhinav J. Maths tutor

8508 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve by factorisation: 2(x^2) - 5x - 12 = 0


Solve 56x + 10 = 60 - 48x


Solve 5x + 10 = 2x(5x + 10)


Let f be a function of a real variable into the real domain : f(x) = x^2 - 2*x + 1. Find the roots and the extremum of the function f.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences