I have looked into solutions of completing the square however the only example questions I can find are such as $$4x^2 – 2x – 5$$ and so on.
In an exam coming up I will have a question like this :
Given that c = 13, find the values of a and b below :
$$\sqrt{1573}(6-\sqrt{5200}) = a + b\sqrt{c}$$
I know that I have to simplify the numbers into their primes to begin with but how do I do that ?
Best Answer
It has nothing to do (directly) with quadratic equations.
Hint:
$1573=11^2\cdot 13$, $\;5200=20^2\cdot 13$.
Some details: $$\sqrt{1573}(6-\sqrt{5200})=11\sqrt{13}(6-20\sqrt{13})=66\sqrt{13}-220\cdot\sqrt{13}^2=\underbrace{-2860}_{\vphantom{b}a}+\underbrace{66}_b\sqrt{13}. $$