id: 06312022
dt: j
an: 2014d.00672
au: Miles, David
ti: A hornetâ€™s nest.
so: Math. Sch. (Leicester) 43, No. 1, 17 (2014).
py: 2014
pu: Mathematical Association (MA), Leicester
la: EN
cc: H34
ut: quadratic equations; nested surds; simplification; completed square;
discriminant; perfect square; solving equations; manipulation of
expressions
ci:
li:
ab: From the text: I set my year 12 further mathematicians a deceptively simple
question as a starter. Prove $1+\sqrt{3}$ is a solution of the
quadratic equation $x^2-4x+2\sqrt{3}=0$ and hence, or otherwise, find
the other solution in its simplest exact form. The first part presented
no difficulty, but I was a little disappointed that no one spotted the
efficient way to tackle the second part.
rv: