(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
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