Question

If $n$ is such that $36 \leq n \leq 72$, then $x = \frac{n^2 + 2\sqrt{n(n+4)} + 16}{n + 4\sqrt{n + 4}}$ satisfies:

• A. $20<x<54$
• B. $23<x<58$
• C. $25<x<64$
• D. $28<x<60$

Hint:

When dealing with inequalities and expressions involving square roots, simplify the expression and substitute the boundary values to determine the correct range.

Answer 1

The Correct Option is C

We are given that $36 \leq n \leq 72$ and the expression for $x$. By simplifying the given expression for $x$ and checking the values for $n$, we find that the range of $x$ falls between $25$ and $64$.