Theory question 103
Functions(a) If f(x + 2) = 6x2 + 5x − 8, find f(5).
(b) Express (7√2 + 3√3)/(4√2 − 2√3) in the form p + q√r, where p, q, and r are rational numbers.
Show the model answer
Model answer
(a) x + 2 = 5 when x = 3: f(5) = 54 + 15 − 8 = 61.
(b) Multiply by (4√2 + 2√3): numerator 56 + 14√6 + 12√6 + 18 = 74 + 26√6; denominator 32 − 12 = 20.
Answer 37/10 + (13/10)√6.
Explanation
In (a) choose x so that x + 2 = 5.