← Olympiad Algebra

Chapter 4

Same degree everywhere

When every term has the same degree, scale doesn't matter: fix one variable, or use the condition to lift every term to the same degree.

1

Scale doesn't matter

Every term of (a² + b²)/ab has degree 2 on top and 2 below. Drag the corner: the rectangle grows, the ratio doesn't.

a = 6b = 3
a2+b2ab\dfrac{a^2+b^2}{ab}==4518\dfrac{45}{18}==2.52.5
Next chapter: Pinned down by very little →