(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.

AJ
Answered by Abhinav J. Maths tutor

8894 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations: 1) 3x+5y=14 and 2) -3y+10=x


Line L goes through point (2,13) and is perpendicular to the line y = 4x-5. Find the equation of line L.


x is inversely proportional to P. When P = 6, x =2. What does x = when P = 4?


Find the positive solution to the equation (x^2+9x+18)/(x^2-9)=10


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences