Review question

# Can we prove these bounds for this fraction involving surds? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7077

## Question

1. The variables $x$ and $y$ are connected by the relation $y = ax^n$, where $a$ and $n$ are constants; $y = 3$ when $x = 4$ and $y = 2$ when $x = 9$. Find the exact values of $n$ and $a$.

1. Express $\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}$ as a fraction having a rational denominator.

2. Show that, if $n$ is a positive integer, then $n(n+2)$ lies between $n^2$ and $(n+1)^2$.

3. If $n$ is a positive integer, use the results in (i) and (ii) to find in terms of $n$ two consecutive integers between which $\frac{\sqrt{n+2}+\sqrt{n}}{\sqrt{n+2}-\sqrt{n}}$ must lie.